# arXiv daily: General Relativity and Quantum Cosmology (gr-qc)

##### 1.Constraints via EHT for black hole solutions with dark matter under the generalized uncertainty principle minimal length scale effect

**Authors:**Ali Övgün, Lemuel John F. Sese, Reggie C. Pantig

**Abstract:** We derived four novel classes of spherically symmetric but non-asymptotically flat black hole solutions surrounded with spherical dark matter distribution perceived under the minimal length scale effect via the Generalized Uncertainty Principle (GUP). Here, we considered the effect of this quantum correction, described by the parameter $\gamma$, on a toy model galaxy with dark matter and the three well-known dark matter distributions: the Cold Dark Matter (CDM), Scalar Field Dark Matter (SFDM), and the Universal Rotation Curve (URC). We aimed to find constraints to $\gamma$ by applying these solutions to the known supermassive black holes: Sgr. A* and M87*, in conjunction with the available Event Horizon telescope. We then examined the effect of $\gamma$ on the event horizon, photonsphere, and shadow radii, where we observed unique deviations from the Schwarzschild case. As for the shadow radii, we obtained bounds for the values of $\gamma$ on each black hole solution at $1\sigma$ confidence level. Our results revealed that under minimal length scale effect, black holes can give positive (larger shadow) and negative values (smaller shadow) of $\gamma$, which are supported indirectly by laboratory experiments and astrophysical or cosmological observations, respectively.

##### 2.Finite-time Cosmological Singularities and the Possible Fate of the Universe

**Authors:**Jaume de Haro, Shin'ichi Nojiri, S. D. Odintsov, V. K. Oikonomou, Supriya Pan

**Abstract:** Singularities in any physical theory are either remarkable indicators of the unknown underlying fundamental theory, or indicate a change in the description of the physical reality. In General Relativity there are three fundamental kinds of singularities that might occur, firstly the black hole spacelike crushing singularities, e.g. in the Schwarzschild case and two cosmological spacelike singularities appearing in finite-time, namely, the Big Bang singularity and the Big Rip singularity. In the case of black hole and Big Bang singularity, the singularity indicates that the physics is no longer described by the classical gravity theory but some quantum version of gravity is probably needed. The Big Rip is a future singularity which appears in the context of General Relativity due to a phantom scalar field needed to describe the dark energy era. Apart from the Big Rip singularity, a variety of finite-time future singularities, such as, sudden singularity, Big Freeze singularity, generalized sudden singularity, $w$-singularity and so on, are allowed in various class of cosmological models irrespective of their origin. The occurrence of these finite-time singularities has been intensively investigated in the context of a variety of dark energy, modified gravity, and other alternative cosmological theories. These singularities suggest that the current cosmological scenario is probably an approximate version of a fundamental theory yet to be discovered. In this review we provide a concrete overview of the cosmological theories constructed in the context of Einstein's General Relativity and modified gravity theories that may lead to finite-time cosmological singularities. We also discuss various approaches suggested in the literature that could potentially prevent or mitigate finite-time singularities within the cosmological scenarios.

##### 3.Coupling Constants as Conserved Charges in Black Hole Thermodynamics

**Authors:**Kamal Hajian, Bayram Tekin

**Abstract:** In a generic theory of gravity coupled to matter fields, the Smarr formula and the first law of thermodynamics of black holes do not work properly if the contributions of the coupling constants defining the theory are not incorporated. However, these couplings, such as the cosmological constant or the dimensionful parameters that appear in the Lagrangian, are fixed parameters defining the theory; and they cannot be varied. Here, we present a robust method, applicable to any covariant Lagrangian, that changes the role of the couplings from the constants in a theory to the free parameters in solutions. To this end, for each one of the couplings in a theory, a pair of auxiliary scalar and gauge fields is introduced. The couplings are shown to be conserved charges of the global part of the implemented gauge symmetry. Besides, their conjugate chemical potentials are defined as the electric potential of the corresponding gauge fields on the black hole horizon. Using this method, we systematically extend the first law and the Smarr formula by coupling conserved charges and their conjugate potentials. The thermodynamics of a black hole solution in a quadratic gravity theory is given as an example.

##### 4.Mass transfer and boson cloud depletion in a binary black hole system

**Authors:**Yao Guo, Wenjie Zhong, Yiqiu Ma, Daiqin Su

**Abstract:** Ultralight boson is one of the potential candidates for dark matter. If exists, it can be generated by a rapidly rotating black hole via superradiance, extracting the energy and angular momentum of the black hole and forming a boson cloud. The boson cloud can be affected by the presence of a companion star, generating fruitful dynamical effects and producing characteristic gravitational wave signals. We study the dynamics of the boson cloud in a binary black hole system, in particular, we develop a framework to study the mass transfer between two black holes. It is found that bosons occupying the growing modes of the central black hole can jump to the decaying modes of the companion black hole, resulting in cloud depletion. This mechanism of cloud depletion is different from that induced by the resonant perturbation from the companion.

##### 5.Scalar-Gauss-Bonnet model, the coincidence problem and the gravitational wave speed

**Authors:**H. Mohseni Sadjadi

**Abstract:** We consider a dark energy model consisting of a scalar field simultaneously coupled to the Gauss-Bonnet invariant and dark matter such that the observational gravitational wave speed constraint on the Gauss-Bonnet term is respected. In the early era, the Gauss-Bonnet term caused the scalar field to remain at a stable point. In this period, dark energy density was negligible. Next, due to the dark matter redshift and the conformal coupling, the initial $Z_2$ symmetry was broken, and the activated field climbed up its potential and provided conditions for late-time acceleration. In this scenario, the Gauss-Bonnet term is not directly involved in the late-time evolution but alleviates the coincidence problem.

##### 6.Freeze-free cosmological evolution with a non-monotonic internal clock

**Authors:**Luis Martinez, Martin Bojowald, Garrett Wendel

**Abstract:** Given the lack of an absolute time parameter in general relativistic systems, quantum cosmology often describes the expansion of the universe in terms of relational changes between two degrees of freedom, such as matter and geometry. However, if clock degrees of freedom (self-)interact non-trivially, they in general have turning points where their momenta vanish. At and beyond a turning point, the evolution of other degrees of freedom is no longer described directly by changes of the clock parameter because it stops and then turns back, while time is moving forward. Previous attempts to describe quantum evolution relative to a clock with turning points have failed and led to frozen evolution in which degrees of freedom remain constant while the clock parameter, interpreted directly as a substitute for monotonic time, is being pushed beyond its turning point. Here, a new method previously used in oscillator systems is applied to a tractable cosmological model, given by an isotropic universe with spatial curvature and scalar matter. The re-collapsing scale factor presents an example of a clock with a single turning point. The method succeeds in defining unitary and freeze-free evolution by unwinding the turning point of the clock, introducing an effective monotonic time parameter that is related to but not identical with the non-monotonic clock degree of freedom. Characteristic new quantum features are found around the turning point, based on analytical and numerical calculations.

##### 1.On a field tensor for gravity and electromagnetism

**Authors:**Mikael Normann

**Abstract:** We show that a three rank Lanczos type tensor field is an appropriate choice to describe relativistic electromagnetic and gravitational effects. More precisely, we identify the irreducible field-decompositions of this tensor as gravitational and electromagnetic fields. A set of divergence equations are proposed as field equations.

##### 2.Quantization of spinor field in the Schwarzschild spacetime and spin sums for solutions of the Dirac equation

**Authors:**Vadim Egorov, Mikhail Smolyakov, Igor Volobuev

**Abstract:** We discuss the problem of canonical quantization of a free massive spinor field in the Schwarzschild spacetime. It is shown that a consistent procedure of canonical quantization of the field can be carried out without taking into account the internal region of the black hole, the canonical commutation relations in the resulting theory hold exactly and the Hamiltonian has the standard form. Spin sums are obtained for solutions of the Dirac equation in the Schwarzschild spacetime.

##### 3.On the existence of a parent theory for General Relativity and Unimodular Gravity

**Authors:**Gerardo García-Moreno, Alejandro Jiménez Cano

**Abstract:** General Relativity (GR) and Unimodular Gravity (UG) provide two equivalent descriptions of gravity that differ in the nature of the cosmological constant. While GR is based on the group of diffeomorphisms that permits the cosmological constant in the action, UG is based on the subgroup of volume-preserving diffeomorphisms together with Weyl transformations which forbid the presence of the cosmological constant. However, the cosmological constant reappears in UG as an integration constant so it arises as a global degree of freedom. Since gauge symmetries are simply redundancies in our description of physical systems, a natural question is whether there exists a "parent theory" with the full diffeomorphisms and Weyl transformations as gauge symmetries so that it reduces to GR and UG respectively by performing suitable (partial) gauge fixings. We will explore this question by introducing Stueckelberg fields both in GR and UG to complete the gauge symmetries in each theory to that of the would-be parent theory. Despite the dynamical equivalence of the two theories, we find that precisely the additional global degree of freedom provided by the cosmological constant in UG obstructs the construction of the parent theory.

##### 4.Near Real-Time Gravitational Wave Data Analysis of the Massive Black Hole Binary with TianQin

**Authors:**Hong-Yu Chen, Xiang-Yu Lyu, En-Kun Li, Yi-Ming Hu

**Abstract:** Space-borne gravitational wave detectors can detect sources like the merger of massive black holes. The rapid identification and localization of the source would play a crucial role in multi-messenger observation. The geocentric orbit of the space-borne gravitational wave detector, TianQin, makes it possible to conduct real-time data transmission. In this manuscript, we develop a search and localization pipeline for massive black hole binaries with TianQin, under both regular and real-time data transmission modes. We demonstrate that with real-time data transmission, it is possible to accurately localize the massive black hole binaries on-the-fly. With the approaching of the merger, the localization rapidly shrinks, and the data analysis can be finished at a speed comparable to the data downlink speed.

##### 5.Relic gravitons and pulsar timing arrays: a theoretical viewpoint

**Authors:**Massimo Giovannini

**Abstract:** During the last three years the pulsar timing arrays reported a series of repeated evidences of gravitational radiation (with stochastically distributed Fourier amplitudes) at a benchmark frequency of the order of $30$ nHz and characterized by spectral energy densities (in critical units) ranging between $10^{-8}$ and $10^{-9}$. While it is still unclear whether or not these effects are just a consequence of the pristine variation of the space-time curvature, the nature of the underlying physical processes would suggest that the spectral energy density of the relic gravitons in the nHz domain may only depend on the evolution of the comoving horizon at late, intermediate and early times. Along this systematic perspective we first consider the most conventional option, namely a post-inflationary modification of the expansion rate. Given the present constraints on the relic graviton backgrounds, we then show that such a late-time effect is unable to produce the desired hump in the nHz region. We then analyze a modified exit of the relevant wavelengths as it may happen when the gravitons inherit an effective refractive index from the interactions with the geometry. A relatively short inflationary phase leads, in this case, to an excess in the nHz region even if the observational data coming from competing experiments do not pin down exactly the same regions in the parameter space. We finally examine an early stage of increasing curvature and argue that it is not compatible with the observed spectral energy density unless the wavelengths crossing the comoving horizon at early times reenter in a decelerated stage not dominated by radiation.

##### 6.Holographic description of the dissipative unified dark fluid model with axion field

**Authors:**I. Brevik, A. V. Timoshkin

**Abstract:** In this article we extend an axion F(R) gravity model, and apply the holographic principle to describe in a unifying manner the early and the late-time universe when the general equation of state (EoS) contains a bulk viscosity. We assume a spatially flat Friedmann-Robertson-Walker (FRW) universe model. We use a description based on the generalized infrared-cutoff holographic dark energy proposed by Nojiri and Odintsov (2006, 2017), and explore the evolution of the universe when the EoS describes the asymptotic behavior between the dust in the early universe and the late universe. We explore various forms of the bulk viscosity, and calculate analytical expressions for the infrared cutoffs in terms of the particle horizon. In this way we obtain a unifying description of the early and the late-time universe in the presence of axion matter, via a viscous holographic fluid model.

##### 7.Prompt sky localization of compact binary sources using meshfree approximation

**Authors:**Lalit Pathak, Sanket Munishwar, Amit Reza, Anand S. Sengupta

**Abstract:** The number of gravitational wave signals from the merger of compact binary systems detected in the network of advanced LIGO and Virgo detectors is expected to increase considerably in the upcoming science runs. Once a confident detection is made, it is crucial to reconstruct the source's properties rapidly, particularly the sky position and chirp mass, to follow up on these transient sources with telescopes operating at different electromagnetic bands for multi-messenger astronomy. In this context, we present a rapid parameter estimation (PE) method aided by mesh-free approximations to accurately reconstruct properties of compact binary sources from data gathered by a network of gravitational wave detectors. This approach builds upon our previous algorithm (Pathak et al.\cite{pathak2022rapid}) to expedite the evaluation of the likelihood function and extend it to enable coherent network PE in a ten-dimensional parameter space, including sky position and polarization angle. Additionally, we propose an optimized interpolation node placement strategy during the start-up stage to enhance the accuracy of the marginalized posterior distributions. With this updated method, we can estimate the properties of binary neutron star (BNS) sources in approximately 2.4~(2.7) minutes for the \TaylorF~(\texttt{IMRPhenomD}) signal model by utilizing 64 CPU cores on a shared memory architecture. Furthermore, our approach can be integrated into existing parameter estimation pipelines, providing a valuable tool for the broader scientific community.

##### 1.Gravitational Radiation from Eccentric Binary Black Hole System in Dynamical Chern-Simons Gravity

**Authors:**Zhao Li, Jin Qiao, Tan Liu, Shaoqi Hou, Tao Zhu, Wen Zhao

**Abstract:** Dynamical Chern-Simons (DCS) gravity, a typical parity-violating gravitational theory, modifies both the generation and propagation of gravitational waves from general relativity (GR). In this work, we derive the gravitational waveform radiated from a binary black hole system with eccentric orbits under the spin-aligned assumption in the DCS theory. Compared with GR, DCS modification enters the second-order post-Newtonian (2PN) approximation, affecting the spin-spin coupling and monopole-quadrupole coupling of binary motion. This modification produces an extra precession rate of periastron. This effect modulates the scalar and gravitational waveform through a quite low frequency. Additionally, the dissipation of conserved quantities results in the secular evolution of the semimajor axis and the eccentricity of binary orbits. Finally, the frequency-domain waveform is given in the post-circular scheme, requiring the initial eccentricity to be $\lesssim0.3$. This ready-to-use template will benefit the signal searches and improve the future constraint on DCS theory.

##### 2.Kinematic and energy properties of dynamical regular black holes

**Authors:**Sebastian Murk, Ioannis Soranidis

**Abstract:** Nonsingular black holes have received much attention in recent years as they provide an opportunity to avoid the singularities inherent to the mathematical black holes predicted by general relativity. Based on the assumption that semiclassical physics remains valid in the vicinity of their horizons, we derive kinematic properties of dynamically evolving spherically symmetric regular black holes. We review the Hawking--Ellis classification of their associated energy-momentum tensors and examine the status of the null energy condition in the vicinity of their horizons as well as their interior. In addition, we analyze the trajectory of a moving observer, find that the horizons can be crossed on an ingoing geodesic, and thus entering and exiting the supposedly trapped spacetime region is possible. We outline the ramifications of this result for the information loss problem and black hole thermodynamics. Throughout the article, we illustrate relevant features based on the dynamical generalization of the regular black hole model proposed in J. High Energy Phys. 09, 118 (2022) and elucidate its connection to the only self-consistent dynamical physical black hole solutions in spherical symmetry.

##### 3.Impact of modified gravity theory on neutron star and nuclear matter properties

**Authors:**Naosad Alam, Subrata Pal, A. Rahmansyah, A. Sulaksono

**Abstract:** New observational data, measured with a high degree of accuracy, of compact isolated neutron stars and binary stars in gravitational wave remnants have the potential to explore the strong field gravity. Within the framework of energy-momentum squared gravity (EMSG) theory we study its impact on several properties of neutron stars and plausible modifications from the predictions of general relativity. Based on a representative set of relativistic nuclear mean field models, non-relativistic Skyrme-Hartree-Fock models and microscopic calculations, we show deviations of neutron star mass-radius sequence in EMSG theory as compared to general relativity. The variation in the effective nuclear equation of state in EMSG, results in distinct magnitudes in the reduced pressure, speed of sound, and maximum compactness at the center of neutron stars. We perform extensive correlation analysis of the nuclear model parameters with the neutron star observables in light of the new observational bounds. Perceptible modifications in the correlations are found in the models of gravity that provide different estimates of the slope and curvature of nuclear matter symmetry energy. The available neutron star data however do not impose stringent enough constraints for clear evidence of deviations from general relativity.

##### 4.Bulk viscous late acceleration under near equilibrium conditions in f(R, T) gravity with mixed matter

**Authors:**Vishnu A Pai, Titus K Mathew

**Abstract:** Various studies have shown that the late acceleration of the universe can be caused by the bulk viscosity associated with dark matter. But recently, it was indicated that a cosmological constant is essential for maintaining Near Equilibrium Conditions (NEC) for the bulk viscous matter during the accelerated expansion of the universe. In the present study, we investigate a model of the universe composed of mixed dark matter components, viscous dark matter (vDM), and inviscid cold dark matter (CDM), in the context of $f(R, T)$ gravity and show that the model predicts late acceleration by satisfying NEC throughout the evolution, without a cosmological constant. We have compared the model predictions with the observational data on Hubble parameter and Type Ia Supernovae.

##### 5.Memory Effect of Gravitational Wave Pulses in PP-Wave Spacetimes

**Authors:**Sucheta Datta, Sarbari Guha

**Abstract:** In this paper we study the memory effect produced in pp-wave spacetimes due to the passage of gravitational wave pulses. We assume the pulse profile in the form of a ramp (which may be considered as an appropriate representation of burst gravitational waves), and analyse its effects on the evolution of nearby geodesics. For a ramp profile, we are able to determine analytical solutions of the geodesic equations in the Brinkmann coordinates. We have plotted the solutions to examine the changes in the separation between a pair of geodesics and their velocity profiles. We find that in the presence of the pulse, the separation (along $ x $ or $ y $-direction) increases monotonically from an initial constant value, whereas the relative velocity grows from zero and settles to a final non-zero constant value. These resulting changes are retained as memory after the pulse dies out. The nature of this memory is found to be similar to that obtained by other workers using Gaussian, square and other pulse profiles, thereby validating the universality of gravitational wave memory.

##### 6.GRFolres: A code for modified gravity simulations in strong gravity

**Authors:**Llibert Aresté Saló, Sam E. Brady, Katy Clough, Daniela Doneva, Tamara Evstafyeva, Pau Figueras, Lorenzo Rossi, Shunhui Yao

**Abstract:** GRFolres is an open-source code for performing simulations in modified theories of gravity, based on the publicly available 3+1D numerical relativity code GRChombo. Note: Submitted for review in the Journal of Open Source Software; Comments welcome; The code can be found at https://github.com/GRChombo/GRFolres

##### 7.Dynamical system analysis of cosmological evolution in the Aether scalar tensor theory

**Authors:**João Luís Rosa, Tom Zlosnik

**Abstract:** The Aether Scalar Tensor (AeST) theory is an extension of General Relativity (GR), proposed for addressing galactic and cosmological observations without dark matter.The action for the theory includes a function that can currently only be constrained by phenomenological considerations. In antecedent work, forms of this function were considered that led to an effective fluid contribution to the cosmological evolution equations that approximated that of dust more and more closely at late cosmic times. In this work we consider an alternative set of functions that most closely approximate dust at the earliest cosmic times and where deviations from dust-like behaviour gradually emerge with time. We use the dynamical system formalism to analyze example models from both possible sets of functions, introducing a complete set of dynamical variables describing the spacetime curvature, energy density parameters of different matter components, and AeST scalar field, and obtain the dynamical equations describing cosmological evolution. The cosmological phase space is found to feature invariant submanifolds associated to the absence of the matter components, as well as equilibrium states associated with well-known cosmological behaviors e.g. matter, radiation, and cosmological constant dominated epochs. A full numerical integration of the dynamical system is performed for the models and it is shown that each can closely approximate the $\Lambda \mathrm{CDM}$ model at the level of the cosmic background. Generalizations of the models are considered and it is shown that the new models likely can simultaneously replicate the cosmological successes of cold dark matter whilst satisfying constraints on the theory from the weak-field quasistatic regime.

##### 8.Teukolsky-like equations in a non-vacuum axisymmetric type D spacetime

**Authors:**Ya Guo, Hiroaki Nakajima, Wenbin Lin

**Abstract:** We study an axisymmetric metric satisfying the Petrov type D property with some additional ansatze, but without assuming the vacuum condition. We find that our metric in turn becomes conformal to the Kerr metric deformed by one function of the radial coordinate. We then study the gravitational-wave equations on this background metric in the case that the conformal factor is unity. We find that under an appropriate gauge condition, the wave equations admit the separation of the variables, and the separated equation for the radial coordinate gives a natural extension of the Teukolsky equation.

##### 9.Asymptotic behavior of solutions and spectrum of states in the quantum scalar field theory in the Schwarzschild spacetime

**Authors:**Mikhail N. Smolyakov

**Abstract:** In this paper, the study of canonical quantization of a free real massive scalar field in the Schwarzschild spacetime is continued. The normalization constants for the eigenfunctions of the corresponding radial equation are calculated, providing the necessary coefficients for the doubly degenerate scatteringlike states that are used in the expansion of the quantum field. It is shown that one can pass to a new type of states such that the spectrum of states with energies larger than the mass of the field splits into two parts. The first part consists of states that resemble properly normalized plane waves far away from the black hole, so they just describe the theory for an observer located in that area. The second part consists of states that live relatively close to the horizon and whose wave functions decrease when one goes away from the black hole. The appearance of the second part of the spectrum, which follows from the initial degeneracy of the scatteringlike states, is a consequence of the topological structure of the Schwarzschild spacetime.

##### 10.Reference Frames and Black Hole Thermodynamics

**Authors:**Franco Fiorini, P. A. González, Yerko Vásquez

**Abstract:** In the context of the absolute parallelism formulation of General Relativity, and because of the fact that the scalar curvature can be written in purely torsional terms, it was known for a long time that a surface term based solely on the torsion tensor appears in the action. It was subsequently suggested that this term might play the role of the Gibbons-Hawking-York boundary term which, in turn, is associated to the free energy in the path integral approach, and then, to the black hole entropy by standard thermodynamic arguments. We show that the identification of the two boundary terms is rather incomplete, and that it strongly depends on the choice of the tetrad (frame) field used to reproduce a given metric. Despite this somewhat awkward situation, we find a class of frames adapted to the Schwarzschild spacetime in which the Gibbons-Hawking-York/torsion link is actually established, and conducing to the right black hole entropy without the need of any background subtraction. Remarkably, these frames are also responsible for the correct value of the gravitational energy as computed from the teleparallel energy-momentum pseudo-current.

##### 11.Unimodular Plebański Gravity

**Authors:**Steffen Gielen, Elliot Nash

**Abstract:** We present new action principles for unimodular gravity, defined in the chiral Pleba\'{n}ski formulation based on (complex) two-forms and a complex ${\rm SO}(3)$ connection. In these theories, just as in their analogues in the metric formulation, the cosmological constant does not take a prescribed value but is an integration constant whose value can differ between different (classical) solutions. We discuss some subtleties when identifying Lorentzian solutions in the generally complex theory, and show how these theories can be reduced to a ``pure connection'' form similar to Krasnov's pure connection formalism for general relativity.

##### 12.Phenomenological footprints of Lambda varying gravity theories inspired from quantum gravity models in the multi-messenger era

**Authors:**Michael R. R. Good, Vasilios Zarikas

**Abstract:** An interesting phenomenological consequence of Lambda varying gravity theories inspired by quantum gravity models is reported. The treatment in the present work is quite general and applicable to several different actions with Lambda varying, especially those used in RG approaches to quantum gravity. An effective gravitational action with a scale varying cosmological constant, Lambda, which depends on the system's characteristics, like the length and the energy density, is the key feature. If the system is an astrophysical object, like a cluster of galaxies, a black hole, etc, non-negligible corrections arise to several observable quantities. Distinctive footprints could refer to luminosity distance and strong/weak lensing measurements, among others. The present study focuses on the SNIa luminosity distance observable.

##### 1.Vacuum Static Spherically Symmetric Spacetimes in Harada's Theory

**Authors:**Alan Barnes

**Abstract:** Very recently Harada proposed a gravitational theory which is of third order in the derivatives of the metric tensor with the property that any solution of Einstein's field equations (EFEs) possibly with a cosmological constant is necessarily a solution of the new theory. He then applied his theory to derive a second-order ODE for the evolution of the scale factor of the FLRW metric. Remarkably he showed that, even in a matter-dominated universe with zero cosmological constant, there is a late-time transition from decelerating to accelerating expansion. Harada also derived a generalisation of the Schwarzschild solution. However, as his starting point he assumed an unnecessarily restricted form for a static spherically symmetric metric. In this note the most general spherically symmetric static vacuum solution of the theory is derived. Mantica and Molinari have shown that Harada's theory may be recast into the form of the EFEs with an additional source term in the form of a second-order conformal Killing tensor(CKT). Accordingly they have dubbed the theory conformal Killing gravity. Then, using a result in a previous paper of theirs on CKTs in generalised Robertson-Walker spacetimes, they rederived Harada's generalised evolution equation for the scale factor of the FLRW metric. However, Mantica and Molinari appear to have overlooked the fact that all solutions of the new theory (except those satisfying the EFEs) admit a non-trivial second-order Killing tensor. Such Killing tensors are invaluable when considering the geodesics of a metric as they lead to a second quadratic invariant of the motion in addition to that derived from the metric.

##### 2.Solutions with pure radiation and gyratons in 3D massive gravity theories

**Authors:**Ercan Kilicarslan, Ivan Kolář

**Abstract:** We find exact solutions of topologically massive gravity (TMG) and new massive gravity (NMG) in ${2+1}$ dimensions (3D) with an arbitrary cosmological constant, pure radiation, and gyratons, i.e., with possibly non-zero $T_{uu}$ and $T_{ux}$ in canonical coordinates. Since any `reasonable' geometry in 3D (i.e., admitting a null geodesic congruence) is either expanding Robinson-Trautman ($\Theta\neq 0$) or Kundt (${\Theta=0}$), we focus on these two classes. Assuming expansions ${\Theta=1/r}$ (`GR-like' Robinson-Trautman) or ${\Theta=0}$ (general Kundt), we systematically integrate the field equations of TMG and NMG and identify new classes of exact solutions. The case of NMG contains an additional assumption of $g_{ux}$ being quadratic in $r$, which is automatically enforced in TMG as well as in 3D GR. In each case, we reduce the field equations as much as possible and identify new classes of solutions. We also discuss various special subclasses and study some explicit solutions.

##### 3.A Bayesian investigation of the neutron star equation-of-state vs. gravity degeneracy

**Authors:**Bhaskar Biswas, Evangelos Smyrniotis, Ioannis Liodis, Nikolaos Stergioulas

**Abstract:** Despite its elegance, the theory of General Relativity is subject to experimental, observational, and theoretical scrutiny to arrive at tighter constraints or an alternative, more preferred theory. In alternative gravity theories, the macroscopic properties of neutron stars, such as mass, radius, tidal deformability, etc. are modified. This creates a degeneracy between the uncertainties in the equation of state (EoS) and gravity since assuming a different EoS can be mimicked by changing to a different theory of gravity. We formulate a hierarchical Bayesian framework to simultaneously infer the EoS and gravity parameters by combining multiple astrophysical observations. We test this framework for a particular 4D Horndeski scalar-tensor theory originating from higher-dimensional Einstein-Gauss-Bonnet gravity and a set of 20 realistic EoS and place improved constraints on the coupling constant of the theory with current observations. Assuming a large number of observations with upgraded or third-generation detectors, we find that the $A+$ upgrade could place interesting bounds on the coupling constant of the theory, whereas with the LIGO Voyager upgrade or the third-generation detectors (Einstein Telescope and Cosmic Explorer), the degeneracy between EoS and gravity could be resolved with high confidence, even for small deviations from GR.

##### 4.An axially symmetric spacetime with causality violation in Ricci-inverse gravity

**Authors:**J. C. R. de Souza, A. F. Santos

**Abstract:** In this paper, Ricci-inverse gravity is investigated. It is an alternative theory of gravity that introduces into the Einstein-Hilbert action an anti-curvature scalar that is obtained from the anti-curvature tensor which is the inverse of the Ricci tensor. An axially symmetric spacetime with causality violation is studied. Two classes of the model are discussed. Different sources of matter are considered. Then a direct relation between the content of matter and causality violation is shown. Our results confirm that Ricci-inverse gravity allows the existence of Closed Time-like Curves (CTCs) that lead to the violation of causality. Furthermore, a comparison is made between the results of general relativity and Ricci-inverse gravity. Other spacetimes, such as G\"{o}del and G\"{o}del-type universes, which are exact solutions of general relativity and allow for causality violations, are also explored in Ricci-inverse gravity framework.

##### 5.Gravitational waves with generalized holonomy corrections

**Authors:**Shulan Li, Jian-Pin Wu

**Abstract:** The cosmological tensor perturbation equation with generalized holonomy corrections is derived in the framework of effective loop quantum gravity. This results in a generalized dispersion relation for gravitational waves, encompassing holonomy corrections. Furthermore, we conduct an examination of the constraint algebra concerning vector modes with generalized holonomy corrections. The requirement of anomaly cancellation for vector modes imposes constraints on the possible functional forms of the generalized holonomy corrections.

##### 6.Transient analysis of arm locking controller

**Authors:**Yi Zhang, Mingzhe Li, Tong Wang, Xinyi Zhao, Long Ma, Shaobo Fang, Ming Xin

**Abstract:** Arm locking is one of the key technologies to suppress the laser phase noise in spaced-based gravitational waves observatories. Since arm locking was proposed, phase margin criterion was always used as the fundamental design strategy for the controller development. In this paper, we find that this empirical method from engineering actually cannot guarantee the arm locking stability. Therefore, most of the advanced arm locking controllers reported so far may have instable problems. After comprehensive analysis of the single arm locking's transient responses, strict analytical stability criterions are summarized for the first time. These criterions are then generalized to dual arm locking, modified-dual arm locking and common arm locking, and special considerations for the design of arm locking controllers in different architectures are also discussed. It is found that PI controllers can easily meet our stability criterions in most of the arm locking systems. Using a simple high gain PI controller, it is possible to suppress the laser phase noise by 5 orders of magnitude within the science band. Our stability criterions can also be used in other feedback systems, where several modules with different delays are connected in parallel.

##### 7.A note on the description of plane gravitational waves in Fermi coordinates

**Authors:**Matteo Luca Ruggiero

**Abstract:** We use the formalism of Fermi coordinates to describe the interaction of a plane gravitational wave in the proper detector frame. In doing so, we emphasize that in this frame the action of the gravitational wave can be explained in terms of a gravitoelectromagnetic analogy. In particular, up to linear displacements from the reference world-line, the effects of the wave on test masses can be described in terms of a Lorentz-like force equation. In this framework we focus on the effects on time measurements provoked by the passage of the wave, and evaluate their order of magnitude. Eventually, we calculate the expression of the local spacetime metric in cylindrical coordinates adapted to the symmetries of the gravitational field and show its relevance in connection with the helicity-rotation coupling.

##### 8.Hidden symmetries of generalised gravitational instantons

**Authors:**Bernardo Araneda

**Abstract:** For conformally K\"ahler Riemannian four-manifolds with a Killing field, we develop a framework to solve the field equations for generalised gravitational instantons corresponding to conformal self-duality and to cosmological Einstein-Maxwell. We obtain generic identities for the curvature of such manifolds without assuming field equations. After applying the framework to recover standard solutions, we find conformally self-dual generalisations of the Page-Pope, Plebanski-Demianski, and Chen-Teo solutions, which are neither hyper-K\"ahler nor quaternionic-K\"ahler, giving new self-dual gravitational instantons in conformal gravity.

##### 9.Rapidly rotating neutron stars: Universal relations and EOS inference

**Authors:**Christian J. Krüger, Sebastian H. Völkel

**Abstract:** We provide accurate universal relations that allow to estimate the moment of inertia $I$ and the ratio of kinetic to gravitational binding energy $T/W$ of uniformly rotating neutron stars from the knowledge of mass, radius, and moment of inertia of an associated non-rotating neutron star. Based on these, several other fluid quantities can be estimated as well. Astrophysical neutron stars rotate to varying degrees and although rotational effects may be neglected in some cases, not modeling them will inevitably introduce bias when performing parameter estimation. This is especially important for future, high-precision measurements coming from electromagnetic and gravitational wave observations. The proposed universal relations facilitate computationally cheap EOS inference codes that permit the inclusion of observations of rotating neutron stars. To demonstrate this, we deploy them into a recent Bayesian framework for equation of state parameter estimation that is now valid for arbitrary, uniform rotation. Our inference results are robust up to around percent level precision for the generated neutron star observations, consisting of the mass, equatorial radius, rotation rate, as well as co- and counter-rotating $f$-mode frequencies, that enter the framework as data.

##### 1.Gravitational wave memory for a class of static and spherically symmetric spacetimes

**Authors:**Soumya Bhattacharya, Shramana Ghosh

**Abstract:** This article aims at comparing gravitational wave memory effect in a Schwarzschild spacetime with that of other compact objects with static and spherically symmetric spacetime, with the purpose of proposing a procedure for differentiating between various compact object geometries. We do this by considering the relative evolution of two nearby test geodesics with in different backgrounds in the presence and absence of a gravitational wave pulse and comparing them. Memory effect due to a gravitational wave would ensure that there is a permanent effect on each spacetime and the corresponding geodesic evolution, being metric dependent, would display distinct results in each case. For a complete picture, we have considered both displacement and velocity memory effect in each geometry.

##### 2.Observations of Orbiting Hot Spots around Naked Singularities

**Authors:**Yiqian Chen, Peng Wang, Haitang Yang

**Abstract:** Recently, it has been reported that photons can traverse naked singularities in the Janis-Newman-Winicour and Born-Infeld spacetimes when these singularities are appropriately regularized. In this paper, we investigate observational signatures of hot spots orbiting these naked singularities, with a focus on discerning them from black holes. In contrast to Schwarzschild black holes, we unveil the presence of multiple additional image tracks within critical curves in time integrated images capturing a complete orbit of hot spots. Moreover, these new images manifest as a more pronounced second-highest peak in temporal magnitudes when observed at low inclinations.

##### 3.Gravitational waves from high-power twisted light

**Authors:**Eduard Atonga, Killian Martineau, Ramy Aboushelbaya, Aurélien Barrau, Marko von der Leyen, Sunny Howard, Abigail James, Jordan Lee, Chunshan Lin, Heath Martin, Iustin Ouatu, Robert Paddock, Rusko Ruskov, Robin Timmis, Peter Norreys

**Abstract:** Recent advances in high-energy and high-peak-power laser systems have opened up new possibilities for fundamental physics research. In this work, the potential of twisted light for the generation of gravitational waves in the high frequency regime is explored for the first time. Focusing on Bessel beams, novel analytic expressions and numerical computations for the generated metric perturbations and associated powers are presented. Compelling evidence is provided that the properties of the generated gravitational waves, such as frequency, polarisation states and direction of emission, are controllable by the laser pulse parameters and optical arrangements.

##### 4.Carter's case [D] admits the 2nd Canonical Form of the Killing Tensor

**Authors:**D. Kokkinos, T. Papakostas

**Abstract:** The study of the Canonical Forms of the Killing Tensor concerns the simultaneous resolving of the Integrability Conditions of the Killing Tensor along with the Einstein's Field Equations employing the framework of Newman-Penrose Formalism. We present all the Petrov Types admitting the 2nd and 3rd Canonical Forms of Killing Tensor in Vacuum in the frame of General Theory of Relativity. During the investigation of the Type D solution of 2nd Canonical form of the Killing Tensor the Carter's Case [D] solution in Vacuum emerged.

##### 5.Uniqueness of the extremal Schwarzschild de Sitter spacetime

**Authors:**David Katona, James Lucietti

**Abstract:** We prove that any analytic vacuum spacetime with a positive cosmological constant in four and higher dimensions, that contains a static extremal Killing horizon with a maximally symmetric compact cross-section, must be locally isometric to either the extremal Schwarzschild de Sitter solution or its near-horizon geometry (the Nariai solution). In four-dimensions, this implies these solutions are the only analytic vacuum spacetimes that contain a static extremal horizon with compact cross-sections (up to identifications). We also consider the analogous uniqueness problem for the four-dimensional extremal hyperbolic Schwarzschild anti-de Sitter solution and show that it reduces to an open problem for the spectrum of the laplacian on compact hyperbolic surfaces.

##### 6.Periapsis precession in general stationary and axisymmetric spacetimes

**Authors:**Jinhong He, Shaofei Xu, Junji Jia

**Abstract:** This work studies the periapsis shift in the equatorial plane of arbitrary stationary and axisymmetric spacetimes. Two perturbative methods are systematically developed. The first work for small eccentricity but very general orbit size and the second, which is post-Newtonian and includes two variants, is more accurate for orbits of large size but allows general eccentricity. Results from these methods are shown to be equivalent under small eccentricity and large size limits. The periapsis shift of Kerr-Newman, Kerr-Sen and Kerr-Taub-NUT spacetimes are computed to high orders. The electric charge and NUT charge are shown to contribute to the leading order but with opposite signs. The frame-dragging term and high-order effect of spacetime spin are given. The electric and NUT changes of the Earth, Sun and Sgr A* are constrained using the Mercury, satellite and S2 precession data. Periapsis shifts of other spacetimes are obtained too.

##### 7.Stability of symmetric teleparallel scalar-tensor cosmologies with alternative connections

**Authors:**Laur Jarv, Laxmipriya Pati

**Abstract:** In symmetric teleparallel geometry the curvature and torsion tensors are assumed to vanish identically, while the dynamics of gravity is encoded by nonmetricity. Here the spatially homogeneous and isotropic connections that can accompany flat Friedmann-Lemaitre-Robertson-Walker metric come in three sets. As the trivial set has received much attention, we focus on the two alternative sets which introduce an extra degree of freedom into the equations. Working in the context of symmetric teleparallel scalar-tensor gravity with generic nonminimal coupling and potential, we show that the extra free function in the connection can not play the role of dark matter nor dark energy, but it drastically alters the scalar field behavior. We determine the restrictions on the model functions which permit the standard cosmological scenario of successive radiation, dust matter, and scalar potential domination eras to be stable. However, the alternative connections also introduce a rather general possibility of the system meeting a singularity in finite time.

##### 8.Fast Bayesian gravitational wave parameter estimation using convolutional neural networks

**Authors:**M. Andrés-Carcasona, M. Martinez, Ll. M. Mir

**Abstract:** The determination of the physical parameters of gravitational wave events is a fundamental pillar in the analysis of the signals observed by the current ground-based interferometers. Typically, this is done using Bayesian inference approaches which, albeit very accurate, are very computationally expensive. We propose a convolutional neural network approach to perform this task. The convolutional neural network is trained using simulated signals injected in a Gaussian noise. We verify the correctness of the neural network's output distribution and compare its estimates with the posterior distributions obtained from traditional Bayesian inference methods for some real events. The results demonstrate the convolutional neural network's ability to produce posterior distributions that are compatible with the traditional methods. Moreover, it achieves a remarkable inference speed, lowering by orders of magnitude the times of Bayesian inference methods, enabling real-time analysis of gravitational wave signals. Despite the observed reduced accuracy in the parameters, the neural network provides valuable initial indications of key parameters of the event such as the sky location, facilitating a multi-messenger approach.

##### 9.General Relativistic Polarized Proca Stars

**Authors:**Zipeng Wang, Thomas Helfer, Mustafa A. Amin

**Abstract:** Massive vector fields can form spatially localized, non-relativistic, stationary field configurations supported by gravitational interactions. The ground state configurations (p-solitons/vector solitons/dark photon stars/polarized Proca stars) have a time-dependent vector field pointing in the same spatial direction throughout the configuration at any instant of time, can carry macroscopic amounts of spin angular momentum, and are spherically symmetric and monotonic in the energy density. In this paper, we include general relativistic effects, and numerically investigate the stability of compact polarized Proca stars (linear and circularly polarized) and compare them to hedgehog-like field configurations (with radially pointing field directions). Starting with approximate field profiles of such stars, we evolve the system numerically using 3+1 dimensional numerical simulations in general relativity. We find that these initial conditions lead to stable configurations. However, at sufficiently large initial compactness, they can collapse to black holes. We find that the initial compactness that leads to black hole formation is higher for circularly polarized stars (which carry macroscopic spin angular momentum), compared to linearly polarized ones, which in turn is higher than that for hedgehog configurations.

##### 10.Can quasi-circular mergers of charged black holes produce extremal black holes?

**Authors:**Gabriele Bozzola, Vasileios Paschalidis

**Abstract:** In contrast to energy and angular momentum, electric charge is conserved in mergers of charged black holes. This opens up the possibility for the remnant to have Kerr-Newman parameter $\chi^{2} + \lambda^{2}$ greater than 1 (with $\chi$ and $\lambda$ being the black hole dimensionless spin and dimensionless charge, respectively), which is forbidden by the cosmic censorship conjecture. In this paper, we investigate whether a naked singularity can form in quasi-circular mergers of charged binary black holes. We extend a theoretical model to estimate the final properties of the remnant left by quasicircular mergers of binary black holes to the charged case. We validate the model with numerical-relativity simulations, finding agreement at the percent level. We then use our theoretical model to argue that while naked singularities cannot form following quasi-circular mergers of non-spinning charged binary black holes, it is possible to produce remnants that are arbitrarily close to the extremal limit.

##### 11.How to Detect an Astrophysical Nanohertz Gravitational-Wave Background

**Authors:**Bence Bécsy, Neil J. Cornish, Patrick M. Meyers, Luke Zoltan Kelley, Gabriella Agazie, Akash Anumarlapudi, Anne M. Archibald, Zaven Arzoumanian, Paul T. Baker, Laura Blecha, Adam Brazier, Paul R. Brook, Sarah Burke-Spolaor, J. Andrew Casey-Clyde, Maria Charisi, Shami Chatterjee, Katerina Chatziioannou, Tyler Cohen, James M. Cordes, Fronefield Crawford, H. Thankful Cromartie, Kathryn Crowter, Megan E. DeCesar, Paul B. Demorest, Timothy Dolch, Elizabeth C. Ferrara, William Fiore, Emmanuel Fonseca, Gabriel E. Freedman, Nate Garver-Daniels, Peter A. Gentile, Joseph Glaser, Deborah C. Good, Kayhan Gültekin, Jeffrey S. Hazboun, Sophie Hourihane, Ross J. Jennings, Aaron D. Johnson, Megan L. Jones, Andrew R. Kaiser, David L. Kaplan, Matthew Kerr, Joey S. Key, Nima Laal, Michael T. Lam, William G. Lamb, T. Joseph W. Lazio, Natalia Lewandowska, Tyson B. Littenberg, Tingting Liu, Duncan R. Lorimer, Jing Luo, Ryan S. Lynch, Chung-Pei Ma, Dustin R. Madison, Alexander McEwen, James W. McKee, Maura A. McLaughlin, Natasha McMann, Bradley W. Meyers, Chiara M. F. Mingarelli, Andrea Mitridate, Cherry Ng, David J. Nice, Stella Koch Ocker, Ken D. Olum, Timothy T. Pennucci, Benetge B. P. Perera, Nihan S. Pol, Henri A. Radovan, Scott M. Ransom, Paul S. Ray, Joseph D. Romano, Shashwat C. Sardesai, Ann Schmiedekamp, Carl Schmiedekamp, Kai Schmitz, Brent J. Shapiro-Albert, Xavier Siemens, Joseph Simon, Magdalena S. Siwek, Sophia V. Sosa Fiscella, Ingrid H. Stairs, Daniel R. Stinebring, Kevin Stovall, Abhimanyu Susobhanan, Joseph K. Swiggum, Stephen R. Taylor, Jacob E. Turner, Caner Unal, Michele Vallisneri, Rutger van Haasteren, Sarah J. Vigeland, Haley M. Wahl, Caitlin A. Witt, Olivia Young

**Abstract:** Analysis of pulsar timing data have provided evidence for a stochastic gravitational wave background in the nHz frequency band. The most plausible source of such a background is the superposition of signals from millions of supermassive black hole binaries. The standard statistical techniques used to search for such a background and assess its significance make several simplifying assumptions, namely: i) Gaussianity; ii) isotropy; and most often iii) a power-law spectrum. However, a stochastic background from a finite collection of binaries does not exactly satisfy any of these assumptions. To understand the effect of these assumptions, we test standard analysis techniques on a large collection of realistic simulated datasets. The dataset length, observing schedule, and noise levels were chosen to emulate the NANOGrav 15-year dataset. Simulated signals from millions of binaries drawn from models based on the Illustris cosmological hydrodynamical simulation were added to the data. We find that the standard statistical methods perform remarkably well on these simulated datasets, despite their fundamental assumptions not being strictly met. They are able to achieve a confident detection of the background. However, even for a fixed set of astrophysical parameters, different realizations of the universe result in a large variance in the significance and recovered parameters of the background. We also find that the presence of loud individual binaries can bias the spectral recovery of the background if we do not account for them.

##### 1.Traversable wormholes in Rastall-Rainbow Gravity

**Authors:**Takol Tangphati, C. R. Muniz, Anirudh Pradhan, Ayan Banerjee

**Abstract:** In this paper, we investigate the existence of asymptotically flat wormhole geometries within the framework of Rastall-Rainbow modified gravity, a synthesis of two distinct theoretical models: Rastall theory and the Rainbow description. Our study uncovers that, when considering specific combinations of free parameters and equations of state, the emergence of static and spherically symmetric wormholes is not feasible within a zero-tidal-force context. By considering the subset of viable solutions, we conduct a rigorous assessment of their stability through adiabatic sound velocity analysis and scrutinize their compliance with the Weak Energy Condition (WEC). In summary, our inquiry provides insights into how the interplay between Rastall parameters and Rainbow functions may alleviate violations of energy conditions in these modified gravity scenarios.

##### 2.Quadrupolar radiation in de Sitter: Displacement memory and Bondi metric

**Authors:**Geoffrey Compère, Sk Jahanur Hoque, Emine Şeyma Kutluk

**Abstract:** We obtain the closed form expression for the metric perturbation around de Sitter spacetime generated by a matter source below Hubble scale both in generalized harmonic gauge and in Bondi gauge up to quadrupolar order in the multipolar expansion, including both parities (i.e. both mass and current quadrupoles). We demonstrate that such a source causes a displacement memory effect close to future infinity that originates, in the even-parity sector, from a $\Lambda$-BMS transition between the two non-radiative regions of future infinity.

##### 3.Wightman function and stochastic gravity noise kernel in impulsive plane wave spacetimes

**Authors:**Hing-Tong Cho

**Abstract:** In this paper we study quantum field theory in impulsive plane wave spacetimes. We first analyze the geodesics and the formation of conjugate planes in these spacetimes. The behaviors of the world function and the van Vleck determinant near conjugate plane are also considered. For the quantum field, we work out the mode functions, their Bogoliubov transformations, and the construction of the Wightman functions. By examining the Wightman function near and on the conjugate plane, we show how the twofold and fourfold singularity structure of the Wigthman function arise when crossing this plane. Lastly, we come to the stochastic gravity noise kernel which is also the correlation function of the stress energy tensor of the quantum field. Its explicit form is given in terms of the world function and the van Vleck determinant. We investigate its limits for small and large geodesic distances. The leading divergent term of the noise kernel on the conjugate plane are expressed in terms of derivatives of delta functions. Similar to that of the Wightman functions, we also examine how the singularity structure of the noise kernel near the lightcone changes when crossing the conjugate plane.

##### 4.Remarks on overestimating the effects of inhomogeneities on the Hubble constant

**Authors:**Taishi Miura, Takahiro Tanaka

**Abstract:** The Hubble constant is one of the most important parameters in cosmology. Discrepancies in values of the Hubble constant estimated from various measurements, the so-called Hubble tension, are a serious problem. In this paper, we study the effects of small-scale inhomogeneities of structure formation on the measurement of the Hubble constant using the luminosity distance-redshift relation. By adopting the adhesion model in Newtonian cosmology as the model of structure formation, we investigate whether or not the effects of inhomogeneities can be sufficiently large to affect the current observations of the Hubble constant. We show that inappropriate treatment of the effects of inhomogeneities can cause a large deviation of the measured value of the Hubble constant from the background value, whose magnitude is comparable with the Hubble tension. Our main message is the importance of adopting an appropriate model of structure formation to investigate the effects of inhomogeneities. We also add discussion on the spatial averaging approach used to estimate the measured Hubble constant in the inhomogeneous universe.

##### 5.Local symmetries as constraints on the motion of freely-falling extended bodies

**Authors:**Abraham I. Harte, David Dwyer

**Abstract:** Different extended objects can fall in different ways, depending on their internal structures. Some motions are nevertheless impossible, regardless of internal structure. This paper derives universal constraints on extended-body motion, both in Newtonian gravity and in general relativity. In both theories, we identify a weak notion of "local symmetry" which precludes certain force and torque combinations. Local symmetries imply that certain components of a body's quadrupole moment cannot affect its motion. They also imply that some forces arise only in combination with appropriate torques. Many of these symmetries are shown to be determined by the algebraic structure of the tidal tensor. In general relativity, we thus relate qualitative features of extended-body motion to the Petrov type of the spacetime. Doing so shows that local symmetries are in fact ubiquitous. In general relativity, there are at least two in all algebraically-special spacetimes. Some of these are generated by Killing vectors and some by conformal Killing-Yano tensors. However, many local symmetries do not fall into either of these classes.

##### 1.Second MAYA Catalog of Binary Black Hole Numerical Relativity Waveforms

**Authors:**Deborah Ferguson, Evelyn Allsup, Surendra Anne, Galina Bouyer, Miguel Gracia-Linares, Hector Iglesias, Aasim Jan, Pablo Laguna, Jacob Lange, Erick Martinez, Filippo Meoni, Ryan Nowicki, Deirdre Shoemaker, Blake Steadham, Max L. Trostel, Bing-Jyun Tsao, Finny Valorz

**Abstract:** Numerical relativity waveforms are a critical resource in the quest to deepen our understanding of the dynamics of, and gravitational waves emitted from, merging binary systems. We present 181 new numerical relativity simulations as the second MAYA catalog of binary black hole waveforms (a sequel to the Georgia Tech waveform catalog). Most importantly, these include 55 high mass ratio (q >= 4), 48 precessing, and 92 eccentric (e > 0.01) simulations, including 7 simulations which are both eccentric and precessing. With these significant additions, this new catalog fills in considerable gaps in existing public numerical relativity waveform catalogs. The waveforms presented in this catalog are shown to be convergent and are consistent with current gravitational wave models. They are available to the public at https://cgp.ph.utexas.edu/waveform.

##### 2.Analytical results for binary dynamics at the first post-Newtonian order in Einstein-Cartan theory with the Weyssenhoff fluid

**Authors:**Vittorio De Falco, Emmanuele Battista

**Abstract:** The quantum spin effects inside matter can be modeled via the Weyssenhoff fluid, which permits to unearth a formal analogy between general relativity and Einstein-Cartan theory at the first post-Newtonian order. In this framework, we provide some analytical formulas pertaining to the dynamics of binary systems having the spins aligned perpendicular to the orbital plane. We derive the expressions of the relative orbit and the coordinate time, which in turn allow to determine the gravitational waveform, and the energy and angular momentum fluxes. The potentialities of our results are presented in two astrophysical applications, where we compute: ($i$) the quantum spin contributions to the energy flux and gravitational waveform during the inspiral phase; ($ii$) the macroscopic angular momentum of one of the bodies starting from the time-averaged energy flux and the knowledge of few timing parameters.

##### 3.Cosmogenesis as symmetry transformation

**Authors:**Adam Balcerzak, Mateusz Lisaj

**Abstract:** We consider the quantized bi-scalar gravity, which may serve as a locally Lorentz invariant cosmological model with varying speed of light and varying gravitational constant. The equation governing the quantum regime for the case of homogeneous and isotropic cosmological setup is a Dirac-like equation which replaces the standard Wheeler-DeWitt equation. We show that particular cosmogenesis may occur as a result of the action of the symmetry transformation which due to Wigner's theorem can either be unitary or antiunitary. We demonstrate that the transition from the pre-big-bang contraction to the post-big-bang expansion - a scenario that also occurs in string quantum cosmologies - can be attributed to the action of charge conjugation, which belongs to the class of antiunitary transformations. We also demonstrate that the emergence of the two classical expanding post-big-bang universe-antiuniverse pairs, each with opposite spin projections, can be understood as being triggered by the action of a unitary transformation resembling the Hadamard gate.

##### 4.Kinematic anisotropies and pulsar timing arrays

**Authors:**Gianmassimo Tasinato

**Abstract:** Doppler anisotropies, induced by our relative motion with respect to the source rest frame, are a guaranteed property of stochastic gravitational wave backgrounds of cosmological origin. If detected by future pulsar timing array measurements, they will provide interesting information on the physics sourcing gravitational waves, which is hard or even impossible to extract from measurements of the isotropic part of the background only. We analytically determine the pulsar response function to kinematic anisotropies, including possible effects due to parity violation, to features in the frequency dependence of the isotropic part of the spectrum, as well as to the presence of extra scalar and vector polarizations. For the first time, we show how the sensitivity to different effects crucially depends on the pulsar configuration with respect to the relative motion among frames. Correspondingly, we propose examples of strategies of detection, each aimed at exploiting future measurements of kinematic anisotropies for characterizing distinct features of the cosmological gravitational wave background.

##### 5.Proof of the Einstein quadrupole formula for solutions of the Einstein-Vlasov system close to Minkowski spacetime

**Authors:**Érik Amorim, Håkan Andréasson, Markus Kunze

**Abstract:** We rigorously derive the quadrupole formula within the context of the Einstein-Vlasov system. The main contribution of this work is an estimate of the remainder terms, derived from well-defined assumptions, with explicitly stated error terms that depend on the solution's boundedness and decay properties, and the distance to the source. The assumptions are linked to established properties of global solutions of the Einstein-Vlasov system as in \cite{LT}. Prior derivations of the quadrupole formula have relied on post-Newtonian analysis and lacked comparisons with global solution properties. The importance of the no-incoming-radiation condition is emphasized underscoring the need for solutions satisfying this condition. This work thus addresses the limitations of existing results and provides motivation for further research on global solution properties of the Einstein-Vlasov system.

##### 6.Non-radial oscillation of anisotropic neutron stars in full general relativity

**Authors:**Sushovan Mondal, Manjari Bagchi

**Abstract:** We investigate non-radial oscillations of anisotropic neutron stars within the framework of general relativity. Our study involves nonrotating, spherically symmetric anisotropic neutron stars as the unperturbed equilibrium configuration. We employ the BSk21 equation of state to describe neutron star matter and introduce a phenomenological ansatz to account for local anisotropy. Through considering small and adiabatic polar perturbations (even parity), we derive oscillation equations from the linearized Einstein equations. Notably, these oscillation equations explicitly incorporate the influence of pressure anisotropy. We calculate the frequencies and damping times of the fundamental (f) mode for various choices of anisotropic pressure strength. Interestingly, we observe that the f-mode frequencies continue to scale linearly with the average density of neutron stars, even in the presence of anisotropy. We conduct a comprehensive analysis of how anisotropy affects both the f-mode frequency and its associated damping time.

##### 7.On the flow of perfect energy tensors

**Authors:**Juan Antonio Sáez, Salvador Mengual, Joan Josep Ferrando

**Abstract:** The necessary and sufficient conditions are obtained for a unit time-like vector field $u$ to be the unit velocity of a divergence-free perfect fluid energy tensor. This plainly kinematic description of a conservative perfect fluid requires considering eighteen classes defined by differential concomitants of $u$. For each of these classes, we get the additional constraints that label the flow of a conservative energy tensor, and we obtain the pairs of functions $\{\rho,p\}$, energy density and pressure, which complete a solution to the conservation equations.

##### 8.Canonical Analysis of General Relativity Formulated with the New Metric f^{ab}=(-g)^αg^{ab}

**Authors:**J. Kluson

**Abstract:** In this short note we investigate canonical formalism for General Relativity which is formulated with the metric f^{ab}=(-g)^\alpha g^{ab}. We find corresponding Hamiltonian and we show that constraint structure is the same as in the standard formulation.

##### 9.On a Class of Exact Arbitrarily Differentiable de Sitter Cores with Kerr Exteriors: Possible gravastar or regular black hole mimickers

**Authors:**Sasa Ilijic, Andrew DeBenedictis

**Abstract:** Within the paradigm of non-perturbative Einstein gravity we study continuous manifolds which possess de Sitter interiors and Kerr exteriors. These manifolds could represent the spacetime of rotating gravastars or other similar black hole mimickers. The scheme presented here allows for a $C^{n}$ transition from the exactly de Sitter interior to the exactly Kerr exterior, with $n$ arbitrarily large. Generic properties that such models must possess are discussed, such as the changing of the topology of the ergosphere from $S^{2}$ to $S^{1}\times S^{1}$. It is shown how in the outer layers of the transition region (the "atmosphere" as it is often called in astrophysics) the dominant/weak and strong energy conditions can be respected. However, much like in the case of its static spherically symmetric gravastar counterpart, there must be some assumptions imposed in the atmosphere for the energy conditions to hold. These assumptions turn out to not be severe. The class of manifolds presented here are expected to possess all the salient features of the fully generic case. Strictly speaking, a number of the results are also applicable to the locally anti-de Sitter core scenario, although we focus on the case of a positive cosmological constant.

##### 1.Kerr black hole shadow casted by the extraordinary light rays with Weyl corrections

**Authors:**Songbai Chen, Jiliang Jing

**Abstract:** We have investigated the equation of motion for photons with Weyl corrections in a Kerr black hole spacetime in the small coupling case. Our results show that Weyl corrections yield phenomena of birefringence. The light rays propagating in the spacetime are separated into the ordinary rays and the extraordinary rays, and the propagation of the latter depends on the corrections. We probe the effects of Weyl corrections on the Kerr black hole shadows casted by the extraordinary rays and find that such corrections result in a weak stretching or squeezing in the vertical direction for the black hole shadows. Finally, we also study the change of the length of the Near-Horizon Extremal Kerr line (NHEK line) with Weyl corrections. These features could help us to understand the electrodynamics with Weyl corrections from black hole shadows.

##### 2.Gravity-induced entanglement between two massive microscopic particles in curved spacetime: I.The Schwarzschild background

**Authors:**Chi Zhang, Fu-Wen Shu

**Abstract:** The experiment involving the entanglement of two massive particles through gravitational fields has been devised to discern the quantum attributes of gravity. In this paper, we present a scheme to extend this experiment's applicability to more generalized curved spacetimes, with the objective of validating universal quantum gravity within broader contexts. Specifically, we direct our attention towards the quantum gravity induced entanglement of mass (QGEM) in astrophysical phenomena, such as particles traversing the interstellar medium. Notably, we ascertain that the gravitational field within curved spacetime can induce observable entanglement between particle pairs in both scenarios, even when dealing with particles significantly smaller than mesoscopic masses. Furthermore, we obtain the characteristic spectra of QGEM across diverse scenarios, shedding light on potential future experimental examinations. This approach not only establishes a more pronounced and extensive manifestation of the quantum influences of gravity compared to the original scheme but also opens avenues for prospective astronomical experiments. These experiments, aligned with our postulates, hold immense advantages and implications for the detection of quantum gravity and can be envisioned for future design.

##### 3.Gravitational Lensing in Modified Gravity: A case study for Fast Radio Bursts

**Authors:**Surajit Kalita, Shruti Bhatporia, Amanda Weltman

**Abstract:** Over the last few decades, a plethora of modifications to general relativity have been proposed to solve a host of cosmological and astrophysical problems. Many modified gravity models are now ruled out with further astrophysical observations; some theories are still viable, with, at best, bounds on their parameters set by observations to date. More recently, observations of Fast Radio Bursts have proven to be remarkably powerful tools to constrain cosmology and fundamental physics. In this work, we consider a generic modified gravity theory and consider the implications for gravitational lensing with Fast Radio Bursts. We use a set of Fast Radio Burst observations to constrain the fraction of dark matter made up of primordial black holes in such a theory. We further show that modified gravity adds a screening effect on gravitational lensing similar to the case when there is plasma in the path of the light ray acting as a scattering screen.

##### 4.Defect wormholes are defective

**Authors:**Joshua Baines
Victoria University of Wellington, Rudeep Gaur
Victoria University of Wellington, Matt Visser
Victoria University of Wellington

**Abstract:** The various "defect wormholes" developed by Klinkhamer have recently attracted considerable attention -- especially in view of the fact that the simplest example, the so-called "vacuum defect wormhole", was claimed to be an everywhere-vacuum everywhere-Ricci-flat exact solution to the Einstein equations. This claim has been conclusively refuted by Feng, and in the current article we take a deeper look at exactly what goes wrong. The central issue is this: Although Klinkhamer's specific representation of the metric g_{ab} is smooth (C^\infty) his inverse metric g^{ab} is not even everywhere continuous (C^0), being undefined at the wormhole throat. This situation implies that one should very carefully investigate curvature tensors at the throat using the Israel--Lanczos--Sen thin-shell formalism. Doing so reveals the presence of a delta-function energy-condition-violating thin shell of matter at the wormhole throat. The "defect wormholes" are thus revealed to be quite ordinary "cut-and-paste" thin-shell wormholes, but represented in a coordinate system which is unfortunately pathological at exactly the same place that all the interesting physics occurs.

##### 5.Thermodynamic Properties of Regular Phantom Black Hole

**Authors:**M. Haditale, B. Malekolkalami

**Abstract:** The Regular Phantom Black Holes (RPBH)s are of theoretical and observational importance, and some properties have been studied. In this work, we study some of the thermodynamical properties such as entropy, and temperature, ... in three asymptotically spacetimes: flat, de--Sitter (dS), and Anti-de Sitter (AdS). Many of the RPBH properties, including horizon radius, are (directly or indirectly) dependent on a scale parameter b. Due to the slightly different structure from Schwarzschild--metrics, the method to express relations between thermodynamical variables requires a new function of the scale parameter. We also imply the local and global thermodynamic stability through the Heat Capacity (HC) and Gibbs Energy (GB), respectively. The calculations and graphs show the results, in the flat background, are very similar to Schwarzschild ones. Also, some results show that the asymptotically AdS-RPBH is more compatible with physical laws than the dS and flat backgrounds.

##### 6.Solving the initial conditions problem for modified gravity theories

**Authors:**Sam E. Brady, Llibert Aresté Saló, Katy Clough, Pau Figueras, Annamalai P. S

**Abstract:** Modified gravity theories such as Einstein scalar Gauss Bonnet (EsGB) contain higher derivative terms in the spacetime curvature in their action, which results in modifications to the Hamiltonian and momentum constraints of the theory. In principle, such modifications may affect the principal part of the operator in the resulting elliptic equations, and so further complicate the already highly non-linear, coupled constraints that apply to the initial data in numerical relativity simulations of curved spacetimes. However, since these are effective field theories, we expect the additional curvature terms to be small, which motivates treating them simply as an additional source in the constraints, and iterating to find a solution to the full problem. In this work we implement and test a modification to the CTT/CTTK methods of solving the constraints for the case of the most general four derivative, parity invariant scalar-tensor theory, and show that solutions can be found in both asymptotically flat/black hole and periodic/cosmological spacetimes, even up to couplings of order unity in the theory. Such methods will allow for numerical investigations of a much broader class of initial data than has previously been possible in these theories, and should be straightforward to extend to similar models in the Horndeski class.

##### 1.Unifying the dark sector through a single matter fluid with non-zero pressure

**Authors:**Peter K. S. Dunsby, Orlando Luongo, Marco Muccino

**Abstract:** We explore a generalised unified dark energy model that incorporates a non-minimal interaction between a tachyonic fluid and an additional scalar field. Specifically, we require that the second field possesses a vacuum energy, introducing an ineliminable offset due to a symmetry-breaking mechanism. After the transition (occurring as due to the symmetry-breaking mechanism of the second field), the corresponding equation of state (EoS) takes the form of a combination between a generalised Chaplygin gas (GCG) component and a cosmological constant contribution. We reinterpret this outcome by drawing parallels to the so-called Murnaghan EoS, widely-employed in the realm of solid-state physics to characterise fluids that, under external pressure, counteract the pressure's effect. We examine the dynamic behaviour of this model and highlight its key distinctions compared to the GCG model. We establish parameter bounds that clarifies the model's evolution across cosmic expansion history, showing that it, precisely, exhibits behaviour akin to a logotropic fluid that eventually converges to the $\Lambda$CDM model in the early universe, while behaving as a logotropic or Chaplygin gas at intermediate and late times respectively. We explain our findings from a thermodynamic perspective, and determine the small perturbations in the linear regime. At very early times, the growth factor flattens as expected while the main departures occur at late times, where the Murnagham EoS results in a more efficient growth of perturbations. We discuss this deviation in view of current observations and conclude that our model is a suitable alternative to the standard cosmological paradigm, introducing the concept of a matter-like field with non-zero pressure.

##### 2.Non-linear Black Hole Ringdowns: an Analytical Approach

**Authors:**Davide Perrone, Thomas Barreira, Alex Kehagias, Antonio Riotto

**Abstract:** Due to the nature of gravity, non-linear effects are left imprinted in the quasi-normal modes generated in the ringdown phase of the merger of two black holes. We offer an analytical treatment of the quasi-normal modes at second-order in black hole perturbation theory which takes advantage from the fact that the non-linear sources are peaked around the light ring. As a byproduct, we describe why the amplitude of the second-order mode relative to the square of the first-order amplitude depends only weakly on the initial condition of the problem.

##### 3.Dynamics of Dwarf Galaxies in Scalar-Tensor-Vector-Gravity

**Authors:**Ivan De Martino

**Abstract:** We have investigated whether the Scalar-Tensor-Vector Gravity theory (STVG) may explain the kinematic of stars in dwarf spheroidal galaxies. STVG modifies General Relativity by adding extra scalar and vector fields with the main aim of replacing dark matter in astrophysical self-gravitating systems. The weak-field limit of STVG brings a Yukawa-like modification to the Newtonian gravitational potential. The modification is modulated by two parameters, $\alpha$ and $\mu$, that represent a redefinition of the gravitational coupling constant and the mass of the additional vector fields, respectively. Thus, adopting the modified gravitational potential arising in the weak-field limit of STVG, we have solved the spherical Jeans equation to predict the line-of-sight velocity dispersion profiles of eight dwarf spheroidal galaxies orbiting around the Milky Way. The predicted profiles are then compared to the data using a Monte Carlo Markov Chain algorithm. Our results pointed out some tensions on the $\alpha$ parameter within the data set, while comparison with previous analysis shows the effectiveness of STVG in replacing dark matter with extra massive fields. Further improvements will require more sophisticated modelling of the line-of-sight velocity dispersion which will be possible as soon as high-precision astrometric data in dwarf spheroidals will become available.

##### 4.Fermion Soliton Stars with Asymmetric Vacua

**Authors:**L. Del Grosso, P. Pani

**Abstract:** Fermion soliton stars are a motivated model of exotic compact objects in which a nonlinear self-interacting real scalar field couples to a fermion via a Yukawa term, giving rise to an effective fermion mass that depends on the fluid properties. Here we continue our investigation of this model within General Relativity by considering a scalar potential with generic asymmetric vacua. This case provides fermion soliton stars with a parametrically different scaling of the maximum mass relative to the model parameters, showing that the special case of symmetric vacua, in which we recover our previous results, requires fine tuning. In the more generic case studied here the mass and radius of a fermion soliton star are comparable to those of a neutron star for natural model parameters at the GeV scale. Finally, the asymmetric scalar potential inside the star can provide either a positive or a negative effective cosmological constant in the interior, being thus reminiscent of gravastars or anti-de Sitter bubbles, respectively. In the latter case we find the existence of multiple, disconnected, branches of solutions.

##### 5.Cosmic Growth in $f(T)$ Teleparallel Gravity

**Authors:**Salvatore Capozziello, Maria Caruana, Gabriel Farrugia, Jackson Levi Said, Joseph Sultana

**Abstract:** Physical evolution of cosmological models can be tested by using expansion data, while growth history of these models is capable of testing dynamics of the inhomogeneous parts of energy density. The growth factor, as well as its growth index, gives a clear indication of the performance of cosmological models in the regime of structure formation of early Universe. In this work, we explore the growth index in several leading $f(T)$ cosmological models, based on a specific class of teleparallel gravity theories. These have become prominent in the literature and lead to other formulations of teleparallel gravity. Here we adopt a generalized approach by obtaining the M\'{e}sz\'{a}ros equation without immediately imposing the subhorizon limit, because this assumption could lead to over-simplification. This approach gives avenue to study at which $k$ modes the subhorizon limit starts to apply. We obtain numerical results for the growth factor and growth index for a variety of data set combinations for each $f(T)$ model.

##### 6.Characteristic formulations of general relativity and applications

**Authors:**Thanasis Giannakopoulos

**Abstract:** General relativity can describe various gravitational systems of astrophysical relevance, like black holes and neutron stars, or even strongly coupled systems through the holographic duality. The characteristic initial (boundary) value problem has numerous applications in general relativity involving numerical studies and is often formulated using Bondi-like coordinates. Well-posedness of the resulting systems of partial differential equations, however, remains an open question. The answer to this question affects the accuracy, and potentially the reliability of conclusions drawn from numerical studies based on such formulations. In the first part of this thesis, we expand our understanding of the hyperbolicity and well-posedness of Bondi-like free evolution systems. We show that several prototype Bondi-like formulations are only weakly hyperbolic and examine the root cause of this result. Consequently, the characteristic initial (boundary) value problem of general relativity in these gauges is rendered ill-posed in the simplest norms one would like to employ. We discuss the implications of this result in accurate gravitational waveform modeling methods and work towards the construction of alternative norms that might be more appropriate. We also present numerical tests that demonstrate weak hyperbolicity in practice and highlight important features to perform them effectively. In the second part, we turn our attention to applications of these formulations to the qualitative behavior of strongly coupled systems via holography.

##### 7.Quasinormal modes of Reissner-Nordström-AdS: the approach to extremality

**Authors:**Filip Ficek, Claude Warnick

**Abstract:** We consider the quasinormal spectrum of scalar and gravitational perturbations of the Reissner-Nordstr\"om-AdS black hole as the horizon approaches extremality. By considering a foliation of the black hole by spacelike surfaces which intersect the future horizon we implement numerical methods which are well behaved up to and including the extremal limit and which admit initial data which is nontrivial at the horizon. As extremality is approached we observe a transition whereby the least damped mode ceases to be oscillatory in time, and the late time signal changes qualitatively as a consequence.

##### 8.Alleviating $H_0$ tension in scalar-tensor and bi-scalar-tensor theories

**Authors:**Maria Petronikolou, Emmanuel N. Saridakis

**Abstract:** We investigate scalar-tensor and bi-scalar-tensor modified theories of gravity that can alleviate the $H_0$ tension. In the first class of theories we show that choosing particular models with shift-symmetric friction term we are able to alleviate the tension by obtaining smaller effective Newton's constant at intermediate times, a feature that cannot be easily obtained in modified gravity. In the second class of theories, which involve two extra propagating degrees of freedom, we show that the $H_0$ tension can be alleviated, and the mechanism behind it is the phantom behavior of the effective dark-energy equation-of-state parameter. Hence, scalar-tensor and bi-scalar-tensor theories have the capability of alleviating $H_0$ tension with both known sufficient late-time mechanisms.

##### 1.Constraining self-interactions of a massive scalar field using scalar gravitational waves from stellar core collapse

**Authors:**Naomichi Asakawa, Yuichiro Sekiguchi

**Abstract:** We perform a comprehensive numerical study of gravitational waves from stellar core collapse in the massive scalar-tensor theory with the cubic and quartic self-interactions of the scalar field. We investigate the dependence of gravitational waves on the self-interaction as well as the mass of the scalar field and the conformal factor. We find that gravitational-wave spectra show a systematic difference between the cubic and quartic self-interactions. We also find that this systematic difference is insensitive to the mass of the scalar field and the conformal factor. Our results indicate that the type of the self-interaction could be constrained by observations of gravitational waves using the future-planned detectors.

##### 2.Quintessence-like features in the late-time cosmological evolution of $f(Q)$ symmetric teleparallel gravity

**Authors:**N. Myrzakulov, M. Koussour, A. Mussatayeva

**Abstract:** In this study, we investigate the cosmological history within the framework of modified $f(Q)$ gravity, which proposes an alternative theory of gravity where the gravitational force is described by a non-metricity scalar. By employing a parametrization scheme for the Hubble parameter, we obtain the exact solution to the field equations in $f(Q)$ cosmology. To constrain our model, we utilize external datasets, including 57 data points from the Hubble dataset, 1048 data points from the SN dataset, and six data points from the BAO dataset. This enables us to determine the best-fit values for the model parameters involved in the parameterization scheme. We analyze the cosmic evolution of various cosmological parameters, including the deceleration parameter, which exhibits the expected behavior in late-time cosmology and changes its signature with redshift. Further, we present the evolution of energy density, EoS parameter, and other geometrical parameters with respect to redshift. Furthermore, we discuss several cosmological tests and diagnostic analyses. Our findings demonstrate that the late-time cosmic evolution can be adequately described without the need for dark energy by employing a parametrization scheme in modified gravity.

##### 3.Einstein vs Hawking: Black hole binaries and cosmological expansion

**Authors:**Aurélien Barrau, Baptiste Blachier, Maxime Lahlou, Andrew Liu, Killian Martineau

**Abstract:** This note aims at investigating two different situations where the classical general relativistic dynamics compete with the evolution driven by Hawking evaporation. We focus, in particular, on binary systems of black holes emitting gravitational waves and gravitons, and on the cosmological evolution when black holes are immersed in their own radiation bath. Several non-trivial features are underlined in both cases.

##### 4.Hawking radiation for detectors in superposition of locations outside a black hole

**Authors:**Jerzy Paczos, Luis C. Barbado

**Abstract:** Hawking radiation is the proposed thermal black-body radiation of quantum nature emitted from a black hole. One common way to give an account of Hawking radiation is to consider a detector that follows a static trajectory in the vicinity of a black hole and interacts with the quantum field of the radiation. In the present work, we study the Hawking radiation perceived by a detector that follows a quantum superposition of static trajectories in Schwarzschild spacetime, instead of a unique well-defined trajectory. We analyze the quantum state of the detector after the interaction with a massless real scalar field. We find that for certain trajectories and excitation levels, there are non-vanishing coherences in the final state of the detector. We then examine the dependence of these coherences on the trajectories followed by the detector and relate them to the distinguishability of the different possible states in which the field is left after the excitation of the detector. We interpret our results in terms of the spatial distribution and propagation of particles of the quantum field.

##### 5.Minisuperspace description of $f(Q)$-cosmology

**Authors:**A. Paliathanasis, N. Dimakis, T. Christodoulakis

**Abstract:** We investigate the existence of minisuperspace description for the homogeneous cosmological field equations within the framework of symmetric teleparallel $f(Q)$-gravity. We consider the background space to be described by the isotropic Friedmann-Lema\^{\i}tre-Robertson-Walker geometry, the anisotropic Kantowski-Sachs and the anisotropic Bianchi III geometries. Across all these models, we establish that the field equations in $f(Q)$-gravity exhibit second-order characteristics in the coincidence gauge and sixth-order characteristics in the non-coincidence gauge. Specifically, within the latter scenario, the dynamic degrees of freedom are attributed to two scalar fields. Finally, as an example of integrability, we derive a vacuum cosmological solution within the non-coincidence gauge.

##### 6.Searching Gravitational-Wave Bursts with Space-Borne Detectors

**Authors:**Zheng Wu, Hui-Min Fan, Yi-Ming Hu, Ik Siong Heng

**Abstract:** The millihertz gravitational wave band is expected to be opened by space-borne detectors like TianQin. Various mechanisms can produce short outbursts of gravitational waves, whose actual waveform can be hard to model. In order to identify such gravitational wave bursts and not to misclassify them as noise transients, we proposed a proof-of-principle energy excess method, that utilized the signal-insensitive channel to veto noise transients. We perform a test on simulated data, and for bursts with a signal-to-noise ratio of 20, even with the contamination of noise transient, our methods can reach a detection efficiency of 97.4% under a false alarm rate of once per year. However, more frequent occurrences of noise transients would lower the detection efficiency.

##### 7.Influence of dark matter equation of state on the axial gravitational ringing of supermassive black holes

**Authors:**Yuqian Zhao, Bing Sun, Zhoujian Cao, Kai Lin, Wei-Liang Qian

**Abstract:** In this work, we explore the effects of surrounding dark matter featuring different equations of state on the axial gravitational quasinormal modes of supermassive black holes situated at the center of galaxies. Our attention primarily rests on dark matter exhibiting a spike structure, originating from relativistic Bondi accretion through an adiabatic process, which diminishes at a certain distance from the black hole. We analyze how varying the equation of state of the dark matter influences the properties of the spacetime in the black hole's vicinity. Our findings reveal that different states of dark matter spikes correspondingly affect the black hole's quasinormal modes. In particular, we identify deviations in both the ringing frequency and damping time, reaching magnitudes of up to $10^{-3}$ for certain parameter values. These variations can potentially be detected by upcoming space-borne detectors. Our findings thus indicate the feasibility of discerning and limiting the essential properties of dark matter surrounding supermassive black holes using future gravitational wave detections, particularly in the case of extreme mass ratio inspiral systems.

##### 1.Superradiance scattering of scalar, electromagnetic, and gravitational fields and thin accretion disk around non-commutating Kerr black hole

**Authors:**Sohan Kumar Jha

**Abstract:** We consider the non-commutative(NC) Kerr black hole where the mass of the central object is smeared over a region of linear size $\sqrt{b}$, $b$ is the strength of the NC character of spacetime. For the spacetime under consideration, we calculate the amplification factor for scalar, electromagnetic, and gravitational fields, and study various properties of a thin accretion disk. The expression for the amplification factor is obtained with the help of the asymptotic matching technique. The amplification factor is then plotted against frequency for various values of the spin $a$ and the NC parameter $b$. We find that though the amplification factor increases with $a$ but decreases with $b$, the cut-off frequency up to which we have amplification increases with $a$ and $b$. We then study the effect of the spin and the NC nature of spacetime on the energy flux, temperature distribution, emission spectrum, energy conversion efficiency, and the radius of the innermost stable circular orbit of a thin accretion disk around the black hole with the help of the steady-state Novikov-Thorne model. Our study reveals that these quantities increase with the spin and the NC parameter. We also find that the disk around the NC Kerr black is hotter and more luminous than that around the Kerr black hole and the NC Schwarzschild black hole. We can conclusively infer from our investigation that the NC nature of spacetime has a significant impact on the superradiance phenomenon as well as on various properties of thin accretion disks.

##### 2.Quantum Field Theory in Curved Spacetime (2nd Edition)

**Authors:**Bernard S. Kay
York

**Abstract:** The 2023 second edition of a 2006 encyclopedia article on mathematical aspects of quantum field theory in curved spacetimes (QFTCST). Section titles [with titles of newly added subsections in square brackets] are: Introduction and preliminaries; Construction of a *-algebra for a real linear scalar field on globally hyperbolic spacetimes and some general theorems, [More about (quasifree) Hadamard states]; Particle creation and the limitations of the particle concept; Theory of the stress-energy tensor; More about the intersection of QFTCST with AQFT and the Fewster-Verch No-Go Theorem; Hawking and Unruh effects, [More about (classical and) quantum fields on black hole backgrounds]; Non-globally hyperbolic spacetimes and the time-machine question, [More about QFT on non-globally hyperbolic spacetimes]; Other related topics and some warnings. The article contains many references. It also includes a review of, and also compares and contrasts, recent results on the implications of QFTCST for the question of the instability of three sorts of Cauchy horizon -- first those inside black holes such as especially Reissner-Nordstr\"om-de Sitter and Kerr-de Sitter, second the compactly generated Cauchy horizons of spacetimes in which time-machines get manufactured, and third the Cauchy horizon of the spacetime diagram which is believed to describe evaporating black holes and which underlies (one version of) the black hole information-loss puzzle.

##### 1.Electromagnetic Multipoles for Morris-Thorne Wormhole

**Authors:**A. H. Hasmani, Sagar V. Soni, Ravi Panchal

**Abstract:** Wormholes are interesting space-time structures connecting two asymptotic regions found in a universe or multiverse and are solutions to Einstein's field equations. These objects have many interesting features as far as physics is concerned. Morris and Thorne introduced traversable wormholes, which increases the possibility of space-time travel. In this work, the wave equation of the Morris-Thorne wormhole has been derived by the technique of differential forms. The solution of the wave equation for a particular choice of red-shift function and shape function is obtained. The potential has also been computed in order to analyze electromagnetic fields. The behavior of electromagnetic multipoles is expressed and investigated in their behavior at the wormhole's throat.

##### 2.Compact binary systems in Einstein-Aether gravity: Direct integration of the relaxed field equations to 2.5 post-Newtonian order

**Authors:**Fatemeh Taherasghari, Clifford M. Will

**Abstract:** The Einstein-Aether theory is an alternative theory of gravity in which the spacetime metric is supplemented by a long-range timelike vector field (the ``aether'' field). Here, for the first time, we apply the full formalism of post-Minkowskian theory and of the Direct Integration of the Relaxed Einstein Equations (DIRE), to this theory of gravity, with the goal of deriving equations of motion and gravitational waveforms for orbiting compact bodies to high orders in a post-Newtonian expansion. Because the aether field is constrained to have unit norm, a naive application of post-Minkowskian theory leads to contributions to the effective energy momentum tensor that are {\em linear} in the perturbative fields. We show that a suitable redefinition of fields using an array of ``superpotentials'' can eliminate such linear terms to any desired post-Newtonian order, resulting in flat spacetime wave equations for all fields, with sources consisting of matter terms and terms quadratic and higher in the fields. As an initial application of this new method, and as a foundation for obtaining the equations of motion for compact binaries, we obtain explicit solutions of the relaxed equations sufficient to obtain the metric in the near zone through 2.5 post-Newtonian order, or $O[(v/c)^5]$ beyond the Newtonian approximation.

##### 3.Scalar Cosmological Perturbations from Quantum Entanglement within Lorentzian Quantum Gravity

**Authors:**Alexander F. Jercher, Luca Marchetti, Andreas G. A. Pithis

**Abstract:** We derive the dynamics of (isotropic) scalar perturbations from the mean-field hydrodynamics of full Lorentzian quantum gravity, as described by a two-sector (timelike and spacelike) Barrett-Crane group field theory (GFT) model. The rich causal structure of this model allows us to consistently implement in the quantum theory the causal properties of a physical Lorentzian reference frame composed of four minimally coupled, massless, and free scalar fields. Using this frame, we are able to effectively construct relational observables that are used to recover macroscopic cosmological quantities. In particular, small isotropic scalar inhomogeneities emerge as a result of (relational) nearest-neighbor two-body entanglement between degrees of freedom of the underlying quantum gravity theory. The dynamical equations we obtain for geometric and matter perturbations show agreement with those of classical general relativity in the long-wavelength, super-horizon limit. In general, deviations become important for sub-horizon modes, which seem to be naturally associated with a trans-Planckian regime in our physical reference frame. We argue that these trans-Planckian corrections are quantum gravitational in nature. However, we explicitly show that for some physically interesting solutions these quantum gravity effects can be quite small, leading to a very good agreement with the classical GR behavior.

##### 4.Are we survivors of the sudden past singularity?

**Authors:**Adam Balcerzak, Tomasz Denkiewicz, Mateusz Lisaj

**Abstract:** In this paper, we investigate the viability of cosmological models featuring a type II singularity that occurs during the past evolution of the Universe. We construct a scenario in which the singularity arises and then constrain the model parameters using observational data from Type Ia Supernovae, Cosmic Chronometers, and Gamma Ray Bursts. We find that the resulting cosmological models based on scenarios with the past type II singularity cannot be excluded by kinematical tests using current observations.

##### 5.Anisotropic Conformal Dark Gravity on the Lorentz Tangent Bundle Spacetime

**Authors:**Christos Savvopoulos, Panayiotis Stavrinos

**Abstract:** In this work we investigate the anisotropic conformal structure of the gravitational field incorporating dark gravity in a generalized Lagrange geometric framework on the Lorentz tangent bundle and we present two applications; the anisotropic conformal Minkowski spacetime and the anisotropic conformal FLRW cosmology. In the first application, the conformal factor induces an anisotropic conformal de-Sitter-like space with extra curvature which causes extra gravity and allows for Sasaki-type Finsler-like structures which could potentially describe certain gravitational phenomena in a more extended form. The cosmological properties of the model are also studied using a FLRW metric structure for the underlying base manifold in the second application, where we derive generalized Friedmann-like equations for the horizontal subspace of the Lorentz tangent bundle spacetime that reduce under certain conditions to those given by A. Triantafyllopoulos and P. C. Stavrinos (2018) [Class. Quantum Grav. 35 085011] as well as those of general relativity.

##### 6.The dynamics of vacuum, gravity and matter: Implications on the fundamental constants

**Authors:**Joan Solà Peracaula

**Abstract:** The possibility that the vacuum energy density (VED), $\rho_{\rm vac}$, could be time dependent in the expanding Universe is intuitively more reasonable than just a rigid cosmological constant for the entire cosmic history. The dynamics of $\rho_{\rm vac}=\rho_{\rm vac}(H)$ as a function of the Hubble rate, $H(t)$, most likely contributes to alleviate cosmological problems and tensions, having also implications on the so-called fundamental `constants' of Nature, which should be slowly drifting with the cosmic expansion owing to the fluctuations of the quantum vacuum. This includes the gravitational `constant' $G$, but also the gauge and Yukawa couplings as well as the particle masses themselves (both of dark matter and baryonic matter). The subtle exchange of energy involved is the basis for the ``micro and macro connection''. Herein, I discuss not only this connection as a possibility but show that it is in fact a generic prediction of QFT in cosmological spacetime which is fully compatible with general covariance. This fact has not been pointed out until recently when an appropriate renormalization framework for the VED has been found which is free from the usual conundrums associated with the cosmological constant problem.

##### 7.MOG as symmetry breaking in Scalar-Vector-Tensor gravity

**Authors:**Shahin Rouhani, Sohrab Rahvar

**Abstract:** The Modified Gravity Model (MOG) has been proposed as a solution to the dark matter problem, but it does not meet the gauge invariant condition. The aim of this work is to propose a gauge-invariant theory, which suggests that symmetry can break at a low temperature in the Universe, leading to the MOG theory. This theory has the potential to alter the dynamics of the early and late Universe and naturally produce cosmological inflation.

##### 1.Light Propagation in the vicinity of the ModMax black hole

**Authors:**Elda Guzman-Herrera, Nora Breton

**Abstract:** ModMax is a nonlinear electrodynamics theory with the same symmetries as Maxwell electrodynamics. Static spherically symmetric solutions have been derived by coupling ModMax electrodynamics with the Einstein equations, which can represent a black hole. In this paper, we analyze light propagation in the vicinity of the ModMax black hole. We determine birefringence, light trajectories, deflection, redshifts, as well as the shadow of the black hole using the effective or optical metric to determine the optical paths of light; comparison is done with the corresponding effects in the neighborhood of the Reissner-Nordstrom black hole, that is the solution to the Einstein-Maxwell equations.

##### 2.Extended black hole thermodynamics from extended Iyer-Wald formalism

**Authors:**Yong Xiao, Yu Tian, Yu-Xiao Liu

**Abstract:** In recent years, there has been significant interest in the field of extended black hole thermodynamics, where the cosmological constant and/or other coupling parameters are treated as thermodynamic variables. Drawing inspiration from the Iyer-Wald formalism, which reveals the intrinsic and universal structure of conventional black hole thermodynamics, we illustrate that a proper extension of this formalism also unveils the underlying theoretical structure of extended black hole thermodynamics. As a remarkable consequence, for any gravitational theory described by a diffeomorphism invariant action, it is always possible to construct a consistent extended thermodynamics using this extended formalism.

##### 3.A short note on Magnetized Black-hole in Non-linear Electrodynamics

**Authors:**H. A. Redekar, R. B. Kumbhar, S. P. Das, K. Y. Rajpure

**Abstract:** We have analyzed the thermodynamic properties of magnetized black-hole in the background of non-linear electrodynamics with two parameters $\beta$ and $\gamma$. We have studied the Bekenstein-Hawking entropy, Hawking temperature, specific heats in two-dimesional surface plots as a function of event horizon ($r_{+}$) and $\gamma$. We showed the variation profiles of the above thermodynamic parameters for $\gamma$ [$ 0 \rightarrow 1$]. We identified regions of parameters for the possible phase-transitions and the stability of the black-holes.

##### 4.$P-v$ criticalities, phase transitions and geometrothermodynamics of charged AdS black holes from Kaniadakis statistics

**Authors:**Giuseppe Gaetano Luciano, Emmanuel Saridakis

**Abstract:** Boltzmann entropy-based thermodynamics of charged anti-de Sitter (AdS) black holes has been shown to exhibit physically interesting features, such as $P-V$ criticalities and van der Waals-like phase transitions. In this work we extend the study of these critical phenomena to Kaniadakis theory, which is a non-extensive generalization of the classical statistical mechanics incorporating relativity. By applying the typical framework of condensed-matter physics, we analyze the impact of Kaniadakis entropy onto the equation of state, the Gibbs free energy and the critical exponents of AdS black holes in the extended phase space. Additionally, we investigate the underlying micro-structure of black holes in Ruppeiner geometry, which reveals appreciable deviations of the nature of the particle interactions from the standard behavior. Our analysis opens up new perspectives on the understanding of black hole thermodynamics in a relativistic statistical framework, highlighting the role of non-extensive corrections in the AdS black holes/van der Waals fluids dual picture.

##### 5.The quantum optics of gravitational waves

**Authors:**Luca Abraho, Francesco Coradeschi, Antonia Micol Frassino, Thiago Guerreiro, Jennifer Rittenhouse West, Enrico Junior Schioppa

**Abstract:** By utilizing quantum optics techniques, we examine the characteristics of a quantum gravitational wave (GW) signature at interferometers. In particular, we study the problem by analyzing the equations of motion of a GW interacting with an idealized interferometer. Using this method, we reconstruct the classical GW signal from a representation of the quantum version of an almost classical monochromatic wave (a single-mode coherent state), then we discuss the experimental signatures of some specific, more general quantum states. We calculate the observables that could be used at future interferometers to probe possible quantum states carried by the gravitational waves.

##### 6.Regular multi-horizon Lee-Wick black holes

**Authors:**Nicolò Burzillà, Breno L. Giacchini, Tibério de Paula Netto, Leonardo Modesto

**Abstract:** In this paper we carry out a detailed analysis of the static spherically symmetric solutions of a sixth-derivative Lee--Wick gravity model in the effective delta source approximation. Previous studies of these solutions have only considered the particular case in which the real and the imaginary part of the Lee--Wick mass $\mu=a +i b$ are equal. However, as we show here, the solutions exhibit an interesting structure when the full parameter space is considered, owing to the oscillations of the metric that depend on the ratio $b/a$. Such oscillations can generate a rich structure of horizons, a sequence of mass gaps and the existence of multiple regimes for black hole sizes (horizon position gaps). In what concerns the thermodynamics of these objects, the oscillation of the Hawking temperature determines the presence of multiple mass scales for the remnants of the evaporation process and may permit the existence of cold black holes with zero Hawking temperature~$T$ and quasi-stable intermediate configurations with $T \approx 0$ and a long evaporation lifetime. For the sake of generality, we consider two families of solutions, one with a trivial shift function and the other with a non-trivial one (dirty black hole). The latter solution has the advantage of reproducing the modified Newtonian-limit metric of Lee--Wick gravity for small and large values of~$r$.

##### 7.On the gravitational energy problem and the energy of photons

**Authors:**J. B. Formiga, João Duarte

**Abstract:** The lack of a well-established solution for the gravitational energy problem might be one of the reasons why a clear road to quantum gravity does not exist. In this paper, the gravitational energy is studied in detail with the help of the teleparallel approach that is equivalent to general relativity. This approach is applied to the solutions of the Einstein-Maxwell equations known as $pp$-wave spacetimes. The quantization of the electromagnetic energy is assumed and it is shown that the proper area measured by an observer must satisfy an equation for consistency. The meaning of this equation is discussed and it is argued that the spacetime geometry should become discrete once all matter fields are quantized, including the constituents of the frame; it is shown that for a harmonic oscillation with wavelength $\lambda_0$, the area and the volume take the form $A=4(N+1/2)l_p^2/n$ and $V=2(N+1/2)l_p^2\lambda_0$, where $N$ is the number of photons, $l_p$ the Planck length, and $n$ is a natural number associated with the length along the $z$-axis of a box with cross-sectional area $A$. The localization of the gravitational energy problem is also discussed. The stress-energy tensors for the gravitational and electromagnetic fields are decomposed into energy density, pressures and heat flow. The resultant expressions are consistent with the properties of the fields, thus indicating that one can have a well-defined energy density for the gravitational field regardless of the principle of equivalence.

##### 8.Rotating charged fluids: theorems and results for Weyl type systems

**Authors:**Marcos L. W. Basso, Vilson T. Zanchin

**Abstract:** We perform a systematic study of rotating charged fluids, and extend several well known theorems regarding static Weyl-type systems which were recently compiled by Lemos and Zanchin [Phys. Rev. D 80, 024010 (2009)] to rotating and axisymmetric systems. Static Weyl-type systems are composed by static charged fluid configurations obeying the Newton-Maxwell or the Einstein-Maxwell systems of equations in which the electric potential $\phi$ and the timelike metric potential $g_{tt}\equiv - W^ 2$ satisfy the Weyl hypothesis, i.e., $W=W(\phi)$. In the present analysis, both the Newton-Maxwell and Einstein-Maxwell theories that describe non-relativistic and relativistic systems, respectively, are used to perform a detailed analysis of the general properties of rotating charged fluids rotating charged dust as well as rotating charged fluids with pressure in four-dimensional spacetimes. In comparison to the static (nonrotating) systems, two additional potentials, a metric potential related to rotation and an electromagnetic potential related to the magnetic field, come into play for rotating systems. In each case, constraints between the fluid quantities and the metric and electromagnetic potentials are identified in order to generalize the theorems holding for static charged systems to rotating charged systems. New theorems regarding equilibrium configurations with differential rotation in both the Newtonian and the relativistic theories are stated and proved. For rigidly rotating charged fluids in the Einstein-Maxwell theory, a new ansatz involving the gradient of the metric potentials and the gradient of the electromagnetic potentials is considered in order to prove new theorems. Such an ansatz leads to new constraints between the fluid quantities and field potentials, so implying new equations of state for the charged fluids.

##### 9.The LISA Data Challenge Radler Analysis and Time-dependent Ultra-compact Binary Catalogues

**Authors:**Kristen Lackeos, Tyson B. Littenberg, Neil J. Cornish, James I. Thorpe

**Abstract:** Context. Galactic binaries account for the loudest combined continuous gravitational wave signal in the Laser Interferometer Space Antenna (LISA) band, which spans a frequency range of 0.1 mHz to 1 Hz. Aims. A superposition of low frequency Galactic and extragalactic signals and instrument noise comprise the LISA data stream. Resolving as many Galactic binary signals as possible and characterising the unresolved Galactic foreground noise after their subtraction from the data are a necessary step towards a global fit solution to the LISA data. Methods. We analyse a simulated gravitational wave time series of tens of millions of ultra-compact Galactic binaries hundreds of thousands of years from merger. This data set is called the Radler Galaxy and is part of the LISA Data challenges. We use a Markov Chain Monte Carlo search pipeline specifically designed to perform a global fit to the Galactic binaries and detector noise. Our analysis is performed for increasingly larger observation times of 1.5, 3, 6 and 12 months. Results. We show that after one year of observing, as many as ten thousand ultra-compact binary signals are individually resolvable. Ultra-compact binary catalogues corresponding to each observation time are presented. The Radler Galaxy is a training data set, with binary parameters for every signal in the data stream included. We compare our derived catalogues to the LISA Data challenge Radler catalogue to quantify the detection efficiency of the search pipeline. Included in the appendix is a more detailed analysis of two corner cases that provide insight into future improvements to our search pipeline.

##### 10.Test the Weak Cosmic Supervision Conjecture in Dark Matter-Black Hole System

**Authors:**Liping Meng, Zhaoyi Xu, Meirong Tang

**Abstract:** There is a possibility that the event horizon of a Kerr-like black hole with perfect fluid dark matter (DM) can be destroyed, providing a potential opportunity for understanding the weak cosmic censorship conjecture of black holes. In this study, we analyze the influence of the intensity parameter of perfect fluid DM on the destruction of the event horizon of a Kerr-like black hole with spinning after injecting test particles and scalar fields. We find that, when test particles are incident on the black hole, the event horizon is destroyed by perfect fluid dark matter for extreme black holes. For nearly extreme black holes, when the dark matter parameter satisfies $\alpha \in \left (-r_{h} , 0\right ) \cup \left ( r_{h} ,+ \infty \right )$ i.e.$(A<0)$, the event horizon of the black hole will not be destroyed; when the dark matter parameter satisfies $\alpha \in\left ( -\infty ,-r_{h} \right ]\cup \left[0,r_{h}\right ]$ i.e.$(A\ge 0)$, the event horizon of the black hole will be destroyed. When a classical scalar field is incident into the black hole in the extremal black hole case, we find that the range of mode patterns of the scalar field that can disrupt the black hole event horizon is different for different values of the ideal fluid dark matter intensity parameter. In the nearly extremal black hole case, through our analysis, we have found when $\alpha\neq0 $ and $\alpha\neq\pm\ r_h$ i.e.$A\neq0$, the event horizon of the black hole can be disrupted. Our research results indicate that dark matter might be capable of breaking the black hole horizon, thus potentially violating the weak cosmic censorship conjecture.

##### 11.Shallow relic gravitational wave spectrum with acoustic peak

**Authors:**Ramkishor Sharma, Jani Dahl, Axel Brandenburg, Mark Hindmarsh

**Abstract:** We study the gravitational wave (GW) spectrum produced by acoustic waves in the early universe, such as would be produced by a first order phase transition, focusing on the low-frequency side of the peak. We confirm with numerical simulations the Sound Shell model prediction of a steep rise with wave number $k$ of $k^9$ to a peak whose magnitude grows at a rate $(H/k_\text{p})H$, where $H$ is the Hubble rate and $k_\text{p}$ the peak wave number, set by the peak wave number of the fluid velocity power spectrum. We also show that hitherto neglected terms give a shallower part with amplitude $(H/k_\text{p})^2$ in the range $H \lesssim k \lesssim k_\text{p}$, which in the limit of small $H/k$ rises as $k$. This linear rise has been seen in other modelling and also in direct numerical simulations. The relative amplitude between the linearly rising part and the peak therefore depends on the peak wave number of the velocity spectrum and the lifetime of the source, which in an expanding background is bounded above by the Hubble time $H^{-1}$. For slow phase transitions, which have the lowest peak wave number and the loudest signals, the acoustic GW peak appears as a localized enhancement of the spectrum, with a rise to the peak less steep than $k^9$. The shape of the peak, absent in vortical turbulence, may help to lift degeneracies in phase transition parameter estimation at future GW observatories.

##### 12.Characterization of the gravitational wave spectrum from sound waves within the sound shell model

**Authors:**Alberto Roper Pol, Simona Procacci, Chiara Caprini

**Abstract:** We compute the gravitational wave (GW) spectrum sourced by the sound waves produced during a first-order phase transition during radiation domination. The correlator of the velocity field is evaluated according to the sound shell model. In our derivation, we include the effects of the expansion of the Universe, showing their importance, in particular for sourcing processes with time duration comparable to the Hubble time. From the exact solution of the GW sourcing integral, we find a causal growth at small frequencies, $\Omega_{\rm GW} \sim k^3$, possibly followed by a linear regime $\Omega_{\rm GW} \sim k$ at intermediate $k$, depending on the phase transition parameters. Around the peak, we find a steep growth that approaches the $k^9$ scaling found in the sound shell model. This growth causes a bump around the GW spectrum peak, which may represent a distinctive feature of GWs produced from acoustic motion, since nothing similar has been observed for vortical turbulence. Nevertheless, we find that the $k^9$ scaling is much less extended than expected in the literature, and it does not necessarily appear. The dependence on the duration of the source, $\tau_{\rm fin} - \tau_*$, is quadratic at small frequencies $k$, and proportional to $\ln^2 (\tau_{\rm fin} {\cal H}_*)$ for an expanding Universe. At frequencies around the peak, the growth is suppressed by a factor $\Upsilon = 1 - 1/(\tau_{\rm fin} {\cal H}_*)$, which becomes linear for short duration. We discuss the linear or quadratic dependence on the source duration for stationary processes, which affects the amplitude of the GW spectrum, both in the causality tail and at the peak, showing that the assumption of stationarity is a very relevant one, as far as the GW spectral shape is concerned. Finally, we present a general semi-analytical template of the resulting GW spectrum, which depends on the parameters of the phase transition.

##### 1.A new five-dimensional vacuum-defect wormhole space-time

**Authors:**Faizuddin Ahmed

**Abstract:** We introduce a novel extension to the Klinkahmer-vacuum defect model by incorporating a fifth spatial coordinate, resulting in a comprehensive five-dimensional wormhole space-time. This extension preserves its status as a vacuum solution to the field equations in five-dimensions. We delve into the behavior of geodesic equations in the proximity of this wormhole, shedding light on its intriguing properties.

##### 2.Binary Black Holes in Modified Gravity

**Authors:**Tiago França

**Abstract:** In this thesis, we use numerical relativity to investigate gravitational waves from binary black holes in extensions of GR. We first study spherically symmetric gravitational collapse in cubic Horndeski theories of gravity. By varying the coupling constants and the initial amplitude of the scalar field, we determine the region in the space of couplings and amplitudes for which it is possible to construct global solutions to the Horndeski theories. Furthermore, we identify the regime of validity of effective field theory (EFT) as the sub-region for which a certain weak coupling condition remains small at all times. We study black hole binary mergers in these cubic Horndeski theories of gravity, treating them fully non-linearly. In the regime of validity of EFT, the mismatch of the gravitational wave strain between Horndeski and GR (coupled to a scalar field) can be larger than $30\%$ in the Advanced LIGO mass range. Initial data and coupling constants are chosen so the theory always remains in the weakly coupled regime. We observe that the waveform in Horndeski theories is shifted by an amount much larger than the smallness parameter that controls initial data. This effect is generic and may be present in other theories of gravity involving higher derivatives. We explore a higher-order curvature correction of GR. Guided by toy models, we develop systems capable of reproducing the low energy behaviour of many such theories with a fully nonlinear/non-perturbative approach. We evolve binary black holes, observing a shift in phase accumulated over time which is not statistically significant when compared to GR, for the methods and coupling used. Finally, we present AHFinder, a flexible multi-purpose tool to find apparent horizons in the open-source numerical relativity code GRChombo.

##### 3.Modified cosmology from quantum deformed entropy

**Authors:**S. Jalalzadeh, H. Moradpour, P. V. Moniz

**Abstract:** In Ref. [S. Jalalzadeh, Phys. Lett. B 829 (2022) 137058], Jalalzadeh established that the thermodynamical entropy of a quantum-deformed black hole with horizon area $A$ can be written as $S_q=\pi\sin\left(\frac{A}{8G\mathcal N} \right)/\sin\left(\frac{\pi}{2\mathcal N} \right)$, where $\mathcal N=L_q^2/L_\text{P}^2$, $L_\text{P}$ being the Planck length and $L_q$ denoting, generically, the q-deformed cosmic event horizon distance $L_q$. Motivated by this, we now extend the framework constructed in [S. Jalalzadeh, Phys. Lett. B 829 (2022) 137058] towards the Friedmann and Raychaudhuri equations describing spatially homogeneous and isotropic universe dynamics. Our procedure in this paper involves a twofold assumption. On the one hand, we take the entropy associated with the apparent horizon of the Robertson-Walker universe in the form of the aforementioned expression. On the other hand, we assume that the unified first law of thermodynamics, $dE=TdS+WdV$, holds on the apparent horizon. Subsequently, we find a novel modified cosmological scenario characterized by quantum-deformed (q-deformed) Friedmann and Raychaudhuri equations containing additional components that generate an effective dark energy sector. Our results indicate an effective dark energy component, which can explain the Universe's late-time acceleration. Moreover, the Universe follows the standard thermal history, with a transition redshift from deceleration to acceleration at $z_\text{tran}=0.5$. More precisely, according to our model, at a redshift of $z = 0.377$, the effective dark energy dominates with a de Sitter universe in the long run. We include the evolution of luminosity distance, $\mu$, the Hubble parameter, $H(z)$, and the deceleration parameter, $q(z)$, versus redshift. Finally, we have conducted a comparative analysis of our proposed model with others involving non-extensive entropies.

##### 4.Relative binning for complete gravitational-wave parameter estimation with higher-order modes and precession, and applications to lensing and third-generation detectors

**Authors:**Harsh Narola, Justin Janquart, Quirijn Meijer, K. Haris, Chris Van Den Broeck

**Abstract:** Once a gravitational wave signal is detected, the measurement of its source parameters is important to achieve various scientific goals. This is done through Bayesian inference, where the analysis cost increases with the model complexity and the signal duration. For typical binary black hole signals with precession and higher-order modes, one has 15 model parameters. With standard methods, such analyses require at least a few days. For strong gravitational wave lensing, where multiple images of the same signal are produced, the joint analysis of two data streams requires 19 parameters, further increasing the complexity and run time. Moreover, for third generation detectors, due to the lowered minimum sensitive frequency, the signal duration increases, leading to even longer analysis times. With the increased detection rate, such analyses can then become intractable. In this work, we present a fast and precise parameter estimation method relying on relative binning and capable of including higher-order modes and precession. We also extend the method to perform joint Bayesian inference for lensed gravitational wave signals. Then, we compare its accuracy and speed to those of state-of-the-art parameter estimation routines by analyzing a set of simulated signals for the current and third generation of interferometers. Additionally, for the first time, we analyze some real events known to contain higher-order modes with relative binning. For binary black hole systems with a total mass larger than $50\, M_{\odot}$, our method is about 2.5 times faster than current techniques. This speed-up increases for lower masses, with the analysis time being reduced by a factor of 10 on average. In all cases, the recovered posterior probability distributions for the parameters match those found with traditional techniques.

##### 5.Destroying the Event Horizon of a Rotating Black-Bounce Black Hole

**Authors:**Lai Zhao, Zhaoyi Xu

**Abstract:** For a rotating black hole to be nonsingular, it means that there are no spacetime singularities at its center. The destruction of the event horizon of such a rotating black hole is not constrained by the weak cosmic censorship conjecture, which may provide possibilities to understand the internal structure of black hole event horizons. In this paper, we investigate the possibility of destroying the event horizon of a rotating Black-Bounce black hole by considering test particles with high angular momentum and scalar fields with large angular momentum, covering the entire range of the rotating Black-Bounce black hole. We analyze the influence of the parameter m on the likelihood of destroying the event horizon in this spacetime. Our analysis reveals that under extreme or near-extreme conditions, the event horizon of this spacetime can potentially be destroyed after the absorption of particles energy and angular momentum, as well as the scattering of scalar fields. Additionally, we find that as the parameter m increases, the event horizon of this spacetime model becomes more susceptible to destruction after the injection of test particles or the scattering of scalar fields.

##### 6.Novel regular black holes: geometry, source and shadow

**Authors:**Anjan Kar
Indian Institute of Technology Kharagpur, India, Sayan Kar
Indian Institute of Technology Kharagpur, India

**Abstract:** We propose a two-parameter, static and spherically symmetric regular geometry, which, for specific parameter values represents a regular black hole. The matter required to support such spacetimes within the framework of General Relativity (GR), is found to violate the energy conditions, though not in the entire domain of the radial coordinate. A particular choice of the parameters reduces the regular black hole to a singular, mutated Reissner-Nordstr\"om geometry. It also turns out that our regular black hole is geodesically complete. Fortunately, despite energy condition violation, we are able to construct a viable source, within the framework of GR coupled to matter, for our regular geometry. The source term involves a nonlinear magnetic monopole in a chosen version of nonlinear electrodynamics. Finally, we obtain the shadow profile of the regular black hole and try to estimate the metric parameters using some recent observational results from the EHT collaboration.

##### 7.Scalar- and Vector Dark Matter Admixed Neutron Stars

**Authors:**Cédric Jockel

**Abstract:** It is believed that dark matter (DM) could accumulate inside neutron stars and significantly change their masses, radii and tidal properties. We study what effect bosonic dark matter, modelled as a massive and self-interacting scalar or vector field, has on neutron stars. We derive equations to compute the tidal deformability of the full Einstein-Hilbert-Klein-Gordon system self-consistently, and probe the influence of the scalar field mass and self-interaction strength on the total mass and tidal properties of the combined system, called fermion boson stars (FBS). We are the first to combine Proca stars with neutron stars to mixed systems of fermions and a vector field in Einstein-Proca theory, which we name fermion Proca stars (FPS). We construct equilibrium solutions of FPS, compute their masses, radii and analyse them regarding their stability and higher modes. We find that FPS tend to be more massive and geometrically larger than FBS for equal boson masses and self-interaction strengths. Both FBS and FPS admit DM core and DM cloud solutions and we find that they can produce degenerate results. Core solutions compactify the neutron star component and lower their tidal deformability, cloud solutions have the inverse effect. Electromagnetic observations of certain cloud-like configurations would appear to violate the Buchdahl limit. The self-interaction strength is found to significantly affect both mass and tidal deformability. We discuss observational constraints and the connection to anomalous detections. We also show how models with an effective equation of state compare to the self-consistent solution of FBS and find the self-interaction strength where both solutions converge sufficiently.

##### 8.Mitigating the effect of population model uncertainty on strong lensing Bayes factor using nonparametric methods

**Authors:**Damon H. T. Cheung, Stefano Rinaldi, Martina Toscani, Otto A. Hannuksela

**Abstract:** Strong lensing of gravitational waves can produce several detectable images as repeated events in the upcoming observing runs, which can be detected with the posterior overlap analysis (Bayes factor). The choice of the binary black hole population plays an important role in the analysis as two gravitational-wave events could be similar either because of lensing or astrophysical coincidence. In this study, we investigate the biases induced by different population models on the Bayes factor. We build up a mock catalogue of gravitational-wave events following a benchmark population and reconstruct it using both non-parametric and parametric methods. Using these reconstructions, we compute the Bayes factor for lensed pair events by utilizing both models and compare the results with a benchmark model. We show that the use of a non-parametric population model gives a smaller bias than parametric population models. Therefore, our study demonstrates the importance of choosing a sufficiently agnostic population model for strong lensing analyses.

##### 9.A Generalized Double Chaplygin Model for Anisotropic Matter: The Newtonian Case

**Authors:**Gabriel Abellán, Angel Rincon, Eduard Sanchez

**Abstract:** In this work, we investigate astrophysical systems in a Newtonian regime using anisotropic matter. For this purpose, we considered that both radial and tangential pressures satisfy a generalized Chaplygin-type equation of state. Using this model, we found the Lane--Emden equation for this system and solved it numerically for several sets of parameters. Finally, we explored the mass supported by this physical system and compared it with the Chandrasekhar mass.

##### 10.Regular black holes from higher-derivative and nonlocal gravity: The smeared delta source approximation

**Authors:**Tibério de Paula Netto, Breno L. Giacchini, Nicolò Burzillà, Leonardo Modesto

**Abstract:** In this work we study static spherically symmetric solutions of effective field equations related to local and nonlocal higher-derivative gravity models, based on the effective delta source approximation. We discuss several possibilities for the equations of state, and how they influence the solutions. In particular, we present an equation of state such that the solutions match the Newtonian-limit metric in both regimes of large and small $r$. A significant part of the work is dedicated to the study of the regularity of the solutions and the comparison with the linearized solutions. Explicit solutions are presented for some cases of local and nonlocal models. The results obtained here can be regarded as a possible link between the previous researches on linearized higher-derivative gravity and the solutions of the nonlinear complete field equations.

##### 1.Resonant detectors of gravitational wave in the linear and quadratic generalized uncertainty principle framework

**Authors:**Sukanta Bhattacharyya, Soham Sen, Sunandan Gangopadhyay

**Abstract:** In this work, we consider a resonant bar detector of gravitational wave in the generalized uncertainty principle (GUP) framework with linear and quadratic momentum uncertainties. The phonon modes in these detectors vibrate due to the interaction with the incoming gravitational wave. In this uncertainty principle framework, we calculate the resonant frequencies and transition rates induced by the incoming gravitational waves on these detectors. We observe that the energy eigenstates and the eigenvalues get modified by the GUP parameters. We also observe non-vanishing transition probabilities between two adjacent energy levels due to the existence of the linear order momentum correction in the generalized uncertainty relation which was not present in the quadratic GUP analysis [\href{http://dx.doi.org/10.1088/1361-6382/abac45}{Class. Quantum Grav. 37 (2020) 195006}]. We finally obtain bounds on the dimensionless GUP parameters using the form of the transition rates obtained during this analysis.

##### 2.Fully consistent rotating black holes in the cubic Galileon theory

**Authors:**Philippe Grandclément

**Abstract:** Configurations of rotating black holes in the cubic Galileon theory are computed by means of spectral methods. The equations are written in the 3+1 formalism and the coordinates are based on the maximal slicing condition and the spatial harmonic gauge. The black holes are described as apparent horizons in equilibrium. It enables the first fully consistent computation of rotating black holes in this theory. Several quantities are extracted from the solutions. In particular, the vanishing of the mass is confirmed. A link is made between that and the fact that the solutions do not obey the zeroth-law of black hole thermodynamics.

##### 3.Tidal properties of neutron stars in scalar-tensor theories of gravity

**Authors:**Gastón Creci, Tanja Hinderer, Jan Steinhoff

**Abstract:** A major science goal of gravitational-wave (GW) observations is to probe the nature of gravity and constrain modifications to General Relativity. An established class of modified gravity theories are scalar-tensor models, which introduce an extra scalar degree of freedom. This affects the internal structure of neutron stars (NSs), as well as their dynamics and GWs in binary systems, where distinct novel features can arise from the appearance of scalar condensates in parts of the parameter space. To improve the robustness of the analyses of such GW events requires advances in modeling internal-structure-dependent phenomena in scalar-tensor theories. We develop an effective description of potentially scalarized NSs on large scales, where information about the interior is encoded in characteristic Love numbers or equivalently tidal deformabilities. We demonstrate that three independent tidal deformabilities are needed to characterize the configurations: a scalar, tensor, and a novel 'mixed' parameter, and develop the general methodology to compute these quantities. We also present case studies for different NS equations of state and scalar properties and provide the mapping between the deformabilities in different frames often used for calculations. Our results have direct applications for future GW tests of gravity and studies of potential degeneracies with other uncertain physics such as the equation of state or presence of dark matter in NS binary systems.

##### 4.The Global Network of Cavities to Search for Gravitational Waves (GravNet): A novel scheme to hunt gravitational waves signatures from the early universe

**Authors:**Kristof Schmieden, Matthias Schott

**Abstract:** The idea of searching for gravitational waves using cavities in strong magnetic fields has recently received significant attention. Specifically, discussions focus on cavities with relatively small volumes, which are currently employed in the search for axions. In this context, we propose a novel experimental scheme that enables the detection of gravitational waves in the GHz regime, which could originate, for example, from primordial black hole mergers. The scheme is based on synchronous measurements of cavity signals from multiple devices operating in magnetic fields at distant locations. While gravitational wave signatures might be detectable in individual cavities, distinguishing them from noise is highly challenging. By analyzing the correlation among signals from several, possibly geographically separated cavities, it is not only possible to significantly enhance the signal-to-noise ratio but also to investigate the source of those gravitational wave signatures. In the context of this proposal, a first demonstration experiment with one superconducting cavity is currently conducted, which is the basis of the proposed data-analysis approaches. On this basis the prospects of GravNet (Global Network of Cavities to Search for Gravitational Waves) are outlined in the paper.

##### 1.Raychaudhuri equation and Bouncing cosmology

**Authors:**Madhukrishna Chakraborty, Subenoy Chakraborty

**Abstract:** The present work deals with an exhaustive study of bouncing cosmology in the background of homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker space-time. The geometry of the bouncing point has been studied extensively and used as a tool to classify the models from the point of view of cosmology. Raychaudhuri equation (RE) has been furnished in these models to classify the bouncing point as regular point or singular point. Behavior of time-like geodesic congruence in the neighbourhood of the bouncing point has been discussed using the Focusing Theorem which follows as a consequence of the RE. An analogy of the RE with the evolution equation for a linear harmonic oscillator has been made and an oscillatory bouncing model has been discussed in this context.

##### 2.Traversable wormholes in $f(R)$ gravity sourced by a cloud of strings

**Authors:**Parangam Goswami, Anshuman Baruah, Atri Deshamukhya

**Abstract:** Wormhole solutions in General Relativity (GR) require \textit{exotic} matter sources that violate the null energy condition (NEC), and it is well known that higher-order modifications of GR and some alternative matter sources can support wormholes. In this study, we explore the possibility of formulating traversable wormholes in $f(R)$ modified gravity, which is perhaps the most widely discussed modification of GR, with two approaches. First, to investigate the effects of geometrical constraints on the global characteristics, we gauge the $rr$-component of the metric tensor, and employ Pad\`{e} approximation to check whether a well-constrained \textit{shape function} can be formulated in this manner. We then derive the field equations with a background of string cloud, and numerically analyse the energy conditions, stability, and amount of exotic matter in this space-time. Next, as an alternative source in a simple $f(R)$ gravity model, we use the background cloud of strings to estimate the wormhole shape function, and analyse the relevant properties of the space-time. These results are then compared with those of wormholes threaded by normal matter in the simple $f(R)$ gravity model considered. The results demonstrate that wormholes with NEC violations are feasible; however, the wormhole space-times in the simple $f(R)$ gravity model are unstable.

##### 3.A Study of Morris-Thorne Wormhole in Einstein-Cartan Theory

**Authors:**Sagar V. Soni, A. C. Khunt, A. H. Hasmani

**Abstract:** This paper focuses on the Einstein-Cartan theory, an extension of general relativity that incorporates a torsion tensor into spacetime. The differential form technique is employed to analyze the Einstein-Cartan theory, which replaces tensors with tetrads. A tetrad formalism, specifically the Newmann-Penrose-Jogia-Griffiths formalism, is used to study the field equations. The energy-momentum tensor is also determined, considering a Weyssenhoff fluid with anisotropic matter. The spin density is derived in terms of the red-shift function. We also examine the energy conditions at the throat of a Morris-Thorne wormhole. The results shed light on the properties of wormholes in the context of the Einstein-Cartan theory, including the energy conditions at the throat.

##### 4.Topological dyonic black holes of massive gravity with generalized quasitopological electromagnetism

**Authors:**Askar Ali, Ali Övgün

**Abstract:** In this paper we investigate new dyonic black holes of massive gravity sourced by generalized quasitopological electromagnetism in arbitrary dimensions. We begin by deriving the exact solution to the field equations defining these black holes and look at how graviton's mass, dimensionality parameter, and quasitopological electromagnetic field affect the horizon structure of anti-de Sitter dyonic black holes. We also explore the asymptotic behaviour of the curvature invariants at both the origin and infinity to analyze the geometric structure of the resultant black holes. We also compute the conserved and thermodynamic quantities of these dyonic black holes with the help of established techniques and known formulas. After investigating the relevancy of first law, we look at how various parameters influence the local thermodynamic stability of resultant black hole solution. We also examine how thermal fluctuations affect the local stability of dyonic black holes in massive gravity. Finally, we study the shadow cast of the black hole.

##### 5.The instability of the inner horizon of the quantum-corrected black hole

**Authors:**Li-Ming Cao, Long-Yue Li, Liang-Bi Wu, Yu-Sen Zhou

**Abstract:** We analyse the stability of the inner horizon of the quantum-corrected black hole which is proposed in loop quantum gravity as the exterior of the quantum Oppenheimer-Snyder and Swiss Cheese models. It is shown that the flux and energy density of a test scalar field measured by free-falling observers are both divergent near the Cauchy horizon. By considering the generalized Dray-'t Hooft-Redmond relation which is independent of the field equation, we find that the mass inflation always happens and the scalar curvature and Kretschmann scalar are also divergent on the inner horizon. These suggest that the inner horizon is unstable and will probably turn into a null singularity. The results support the strong cosmic censorship hypothesis. However, this also implies that the quantum corrected model may not be the definitive endpoint as a regular black hole. Besides, it further proposes that any possible observable astronomical phenomenon which depends on the existence of the inner horizon of the black hole is not reliable.

##### 6.Exploring the Quantum-to-Classical Vortex Flow: Quantum Field Theory Dynamics on Rotating Curved Spacetimes

**Authors:**Patrik Švančara, Pietro Smaniotto, Leonardo Solidoro, James F. MacDonald, Sam Patrick, Ruth Gregory, Carlo F. Barenghi, Silke Weinfurtner

**Abstract:** Gravity simulators offer the prospect of emulating quantum field dynamics on curved spacetime, including that of a black hole, in tabletop experiments. Since black holes in nature spin, to simulate a realistic black hole we must be able to achieve rotation - crucially requiring a set-up with at least 2+1 dimensions. Here, we report on the realisation of a draining flow of superfluid helium, with the most extensive stable vortex structures ever observed in a quantum fluid. Our non-contact 3-D measurement technique visualises micrometre-scale interface waves on the superfluid vortex flow, uncovering novel wave-vortex interactions, such as intricate patterns like bound states, and even, potentially, black hole ringdown signatures. This novel approach provides an arena to explore quantum-to-classical vortex flow transitions and develop finite temperature quantum field theory simulators for rotating curved spacetimes.

##### 7.Testing of K(R,T)-gravity through gravastar configurations

**Authors:**GRP Teruel, Ksh. Newton Singh, Tanmoy Chowdhury, Farook Rahaman, Monimala Mondal

**Abstract:** In this article, we are reporting for the first time the existence of gravastar configurations in the framework of K(R,T)-gravity, which can be treated as an alternative to a black hole (Mazur and Mottola). This strengthens how much this new gravity theory may be physically demanding to the gravity community in the near future. We first develop the gravastar field equations for a generic K(R,T) functional and then we study four different models within this theory. We find that the solutions for the interior region are regular everywhere regardless of the exact form of the K(R,T) functional. The solutions for the shell region indicate that two of the four models subjected to the study are physically feasible. In addition, the junction conditions are considered at each interface by using the Lanczos equations that yield the surface density and pressure at the thin shell. We investigate various characteristics of the gravastar structure such as the proper length, energy, and entropy of the spherical distribution.

##### 8.Dust collapse in asymptotic safety: a path to regular black holes

**Authors:**Alfio Bonanno, Daniele Malafarina, Antonio Panassiti

**Abstract:** Regular black hole spacetimes are obtained from an effective Lagrangian for Quantum Einstein Gravity. The interior matter is modeled as a dust fluid, which interacts with the geometry through a multiplicative coupling function denoted as $\chi$. The specific functional form of $\chi$ is deduced from Asymptotically Safe gravity, under the key assumption that the Reuter fixed point remains minimally affected by the presence of matter. As a consequence the gravitational coupling vanishes at high energies. The static exterior geometry of the black hole is entirely determined by the junction conditions at the boundary surface. Consequently, the resulting global spacetime geometry remains devoid of singularities at all times. This result offers a novel perspective on regular black holes in Asymptotically Safe gravity.

##### 1.Insights and guidelines on the Cauchy horizon theorems

**Authors:**Xiao Yan Chew, Dong-han Yeom

**Abstract:** Recently there is progress to resolve the issue regarding the non-existence of the Cauchy horizon inside the static, charged, and spherically symmetric black holes. However, when we generically extend the black holes' spacetime, they are not just static but can be dynamical, thus the interior of black holes does not remain the same as the static case when we take into account the dynamical evolution of black holes. Then, our aim in this paper is to provide a few constructive insights and guidelines regarding this issue by revisiting a few examples of the gravitational collapse of spherically symmetric charged black holes using the double-null formalism. Our numerical results demonstrate that the inside of the outer horizon is no longer static even in late time, and the inner apparent horizon exists but is not regular. The inner apparent horizon can be distinguished clearly from the Cauchy horizon. The spherical symmetric property of black holes allows the inner horizon to be defined in two directions, i.e., the differentiation of the areal radius vanishes along either the out-going or the in-going null direction. Moreover, the Cauchy horizon can be generated from a singularity. Still, the notion of the singularity can be subtle where it can have a vanishing or non-vanishing areal radius; the corresponding curvature quantities could be finite or diverge, although the curvatures can be greater than the Planck scale. Finally, we show some examples that the "hair" which is associated with the matter field on the inner horizon is not important to determine the existence of the Cauchy horizon; rather, the hair on the outer horizon might play an important role on the Cauchy horizon. Therefore, the dynamic properties of the interior of charged black holes could shed light for us to understand deeply about the Cauchy horizon for the extensions of no-Cauchy-horizon theorems.

##### 2.Holomorphic General Coordinate Invariant Modified Measure Gravitational Theory

**Authors:**Eduardo Guendelman

**Abstract:** Complexifying space time has many interesting applications, from the construction of higher dimensional unification, to provide a useful framework for quantum gravity and to better define some local symmetries that suffer singularities in real space time. In this context here spacetime is extended to complex spacetime and standard general coordinate invariance is also extended to complex holomorphic general coordinate transformations. This is possible by introducing a non Riemannian Measure of integration, which transforms avoiding non holomorphic behavior . Instead the measure transforms according to the inverse of the jacobian of the coordinate transformation and avoids the traditional square root of the determinant of the metric $\sqrt{-g}$. which is not globally holomorphic , or the determinant of the vierbein which is sensitive to the vierbein orientations and not invariant under local lorentz transformations with negative determinants. It is impossible to introduce a cosmological constant term in the complex holomorphic invariant theory action, but a cosmological term appears as an integration constant in the equations of motion. The ideas can be generalized to theories of extended objects.

##### 3.Power spectrum with $k^6$ growth for primordial black holes

**Authors:**Rongrong Zhai, Hongwei Yu, Puxun Wu

**Abstract:** The decrease of both the rolling speed of the inflaton and the sound speed of the curvature perturbations can amplify the curvature perturbations during inflation so as to generate a sizable amount of primordial black holes. In the ultraslow-roll inflation scenario, it has been found that the power spectrum of curvature perturbations has a $k^4$ growth. In this paper, we find that when the speed of sound decreases suddenly, the curvature perturbations becomes scale dependent in the infrared limit and the power spectrum of the curvature perturbation only has a $k^2$ growth. Furthermore, by studying the evolution of the power spectrum in the inflation model, in which both the sound speed of the curvature perturbations and the rolling speed of the inflaton are reduced, we find that the power spectrum is nearly scale invariant at the large scales to satisfy the constraint from the cosmic microwave background radiation observations, and at the same time can be enhanced at the small scales to result in an abundant formation of primordial black holes. In the cases of the simultaneous changes of the sound speed and the slow-roll parameter $\eta$ and the change of the sound speed preceding that of the slow-roll parameter $\eta$, the power spectrum can possess a $k^6$ growth under certain conditions, which is the steepest growth of the power spectrum reported so far.

##### 4.Rationalizing Unphysical Radiation in the Unruh Effect by Extending Black Hole Spacetime

**Authors:**Yi-Bo Liang, Hong-Rong Li

**Abstract:** We demonstrate that Schwarzschild spacetime has a conformal extension and that, beyond null infinity, there is a black hole with a timelike singularity. In conformal extended spacetime, every null infinity is a killing horizon with vanishing surface gravity. When a quantized massless scalar field is taken into this spacetime and different vacuums for the field are defined, thermal radiation coming from the extended black hole could be observed. This makes sense, much like the thermal radiation coming from the white hole. The Unruh effect is therefore plausible in conformal extended Schwarzschild spacetime. It is shown that the thermal radiation coming from past null infinity in Schwarzschild spacetime, which is difficult to imagine as the result of any physical process, is the result of the reduction of the thermal radiation passing through past null infinity in conformal extended spacetime. We also present a conformal extension of Kerr spacetime for the first time. Then, by examining a quantized massless scalar field on this spacetime, we get the meaningful conclusion that there is thermal radiation coming from a different rotating black hole passing through past null infinity. Similarly, the result of the Kerr black hole is consistent with that of the Schwarzschild black hole.

##### 5.Observational predictions of inflationary model in spatially covariant gravity with two tensorial degrees of freedom for gravity

**Authors:**Saikat Chakraborty, Khamphee Karwan, Jakkrit Sangtawee

**Abstract:** We study the inflationary model constructed from a Spatially Covariant Gravity (SCG). The Lagrangian for the SCG in our consideration is expressed as the polynomial of irreducible SCG monomials where the total number of derivatives of each monomial is two, and the theory propagates two tensorial degrees of freedom of gravity up to the first order in cosmological perturbations. The condition for having two tensorial degrees of freedom studied earlier in literature for such theories is derived in vacuum. We extend the condition for having two tensorial degrees of freedom to the case where a scalar field is included by imposing a gauge-fixing. We apply the resulting SCG to describe inflationary universe. The observational predictions such as the scalar spectral index and tensor-to-scalar ratio from this model are investigated. We find that the tensor-to-scalar ratio in this model can either be in the order of unity or be small depending on the parameter of the model.

##### 6.Connections between Weyl geometry, quantum potential and quantum entanglement

**Authors:**Shi-Dong Liang, Wenjing Huang

**Abstract:** The Weyl geometry promises potential applications in gravity and quantum mechanics. We study the relationships between the Weyl geometry, quantum entropy and quantum entanglement based on the Weyl geometry endowing the Euclidean metric. We give the formulation of the Weyl Ricci curvature and Weyl scalar curvature in the $n$-dimensional system. The Weyl scalar field plays a bridge role to connect the Weyl scalar curvature, quantum potential and quantum entanglement. We also give the Einstein-Weyl tensor and the generalized field equation in 3D vacuum case, which reveals the relationship between Weyl geometry and quantum potential. Particularly, we find that the correspondence between the Weyl scalar curvature and quantum potential is dimension-dependent and works only for the 3D space, which reveals a clue to quantize gravity and a understanding why our space must be 3D if quantum gravity is compatible with quantum mechanics. We analyze numerically a typical example of two orthogonal oscillators to reveal the relationships between the Weyl scalar curvature, quantum potential and quantum entanglement based on this formulation. We find that the Weyl scalar curvature shows a negative dip peak for separate state but becomes a positive peak for the entangled state near original point region, which can be regarded as a geometric signal to detect quantum entanglement.

##### 7.Stability of Non-Minimally Coupled Topological-Defect Boson Stars

**Authors:**Gray D. Reid, Matthew W. Choptuik

**Abstract:** As shown by Marunovic and Murkovic, non-minimal d-stars, composite structures consisting of a boson star and a global monopole non-minimally coupled to the general relativistic field, can have extremely high gravitational compactness. In a previous paper we demonstrated that these ground-state stationary solutions are sometimes additionally characterized by shells of bosonic matter located far from the center of symmetry. In order to investigate the question of stability posed by Marunovic and Murkovic, we investigate the stability of several families of d-stars using both numerical simulations and linear perturbation theory. For all families investigated, we find that the most highly compact solutions, along with those solutions exhibiting shells of bosonic matter, are unstable to radial perturbations and are therefore poor candidates for astrophysically-relevant black hole mimickers or other highly compact stable objects.

##### 8.Notes on Gravitational Physics

**Authors:**John L. Friedman

**Abstract:** These notes are self-contained, with the first six chapters used for a one-semester course with recommended texts by Wald, Misner, Thorne, and Wheeler (MTW), and, particularly for gravitational waves, by Schutz and by Thorne and Blandford. In its treatment of topics covered in these standard texts, the presentation here typically includes steps between equations that are skipped in Wald or MTW. Treatments of gravitational waves, particle orbits in black-hole backgrounds, the Teukolsky equation, and the initial value equations are motivated in part by the dramatic discoveries of gravitational waves from the inspiral and coalescence of binary black holes and neutron stars, advances in numerical relativity, and the expected launch of the LISA space-based observatory. Students are assumed to have encountered special relativity, but these notes give a detailed presentation with a geometrical orientation, starting with with time dilation and length contraction and including relativistic particles, fluids, electromagnetism, and curvilinear coordinates. Chaps. 2-5 cover curvature, the Einstein equation, relativistic stars, and black holes. Chap. 6, on gravitational waves, includes a discussion of detection and of noise in interferometric detectors. Chap. 7, on the initial value problem, has a section on the form of the equations used in numerical relativity. Its notation is that used, for example, in Baumgarte and Shapiro and Shibata; the presentation here is taken in part from the text by Friedman and Stergioulas. The notes also have a chapter on the Newman-Penrose formalism and the Teukolsky equation. Following that is a chapter on black-hole thermodynamics and a final chapter on the gravitational action and on conserved quantities for asymptotically flat spacetimes, using Noether's theorem.

##### 1.Existence of non-exotic traversable wormholes in squared trace extended gravity theory

**Authors:**S. K. Tripathy, D. Nayak, B. Mishra, D. Behera, S. K. Sahu

**Abstract:** An extended gravity theory is used to explore the possibility of non-exotic matter traversable wormholes. In the extended gravity theory, additional terms linear and quadratic in the trace of the energy momentum tensor are considered in the Einstein-Hilbert action. Obviously, such an addition leads to violation of the energy-momentum tensor. The model parameters are constrained from the structure of the field equations. Non-exotic matter wormholes tend to satisfy the null energy conditions. We use two different traversable wormhole geometries namely an exponential and a power law shape functions to model the wormholes. From a detailed analysis of the energy conditions, it is found that, the existence of non-exotic matter traversable wormholes is not obvious in the model considered and its possibility may depend on the choice of the wormhole geometry. Also, we found that, non-exotic wormholes are possible within the given squared trace extended gravity theory for a narrow range of the chosen equation of state parameter.

##### 2.Non-local tails in radiation in odd dimensions

**Authors:**M. Khlopunov

**Abstract:** Huygens principle violation in a spacetime of odd dimensions leads to the fact that the retarded massless fields of localised sources depend on their history of motion preceding the retarded time. This non-local character of retarded fields should result into the formation of tail signals in the radiation of localised sources. In particular, in gravity theories with odd number of extra spacetime dimensions the gravitational radiation of binary systems should contain the tail terms. In this work, we demonstrate the presence of tail signal in radiation within a simple model of scalar field interacting with the point charge moving on elliptical orbit in three dimensions. We find that the tail term results into the characteristic dependence of radiation power of the charge on time. In particular, its extremum points do not correspond to the moments when the charge passes the pericenter and apocenter of the orbit, in contrast with the four-dimensional theory. We obtain the formulae for the shifts of radiation power extremum points up to the contributions quadratic in the orbital eccentricity. We also compute the spectral distribution of radiation power of the charge. We find that in three dimensions the charge on elliptical orbit radiates into the lower harmonics of the spectrum, compared to the four-dimensional theory. We conjecture that in higher dimensions the character of spectral distributions is opposite - the charge mainly radiates into the higher harmonics of the spectrum.

##### 3.Probing Spin-Induced Quadrupole Moments in Precessing Compact Binaries

**Authors:**Zhenwei Lyu, Michael LaHaye, Huan Yang, Béatrice Bonga

**Abstract:** Spin-induced quadrupole moments provide an important characterization of compact objects, such as black holes, neutron stars and black hole mimickers inspired by additional fields and/or modified theories of gravity. Black holes in general relativity have a specific spin-induced quadrupole moment, with other objects potentially having differing values. Different values of this quadrupole moment lead to modifications of the spin precession dynamics, and consequently modifications to the inspiral waveform. Based on the spin-dynamics and the associated precessing waveform developed in our previous work, we assess the prospects of measuring spin-induced moments in various black hole, neutron star, and black-hole mimicker binaries. We focus on binaries in which at least one of the objects is in the mass-gap (similar to the $2.6 M_\odot$ object found in GW190814). We find that for generic precessing binaries, the effect of the spin-induced quadrupole moments on the precession is sensitive to the nature of the mass-gap object, i.e., whether it is a light black hole or a massive neutron star. So that this is a good probe of the nature of these objects. For precessing black-hole mimicker binaries, this waveform also provides significantly tighter constraints on their spin-induced quadrupole moments than the previous results obtained without incorporating the precession effects of spin-induced quadrupole moments. We apply the waveform to sample events in GWTC catalogs to obtain better constraints on the spin-induced quadrupole moments, and discuss the measurement prospects for events in the O$4$ run of the LIGO-Virgo-KAGRA collaboration.

##### 4.Thermodynamics of the three-dimensional black hole with torsion

**Authors:**Luis Avilés, Diego Hidalgo, Omar Valdivia

**Abstract:** The stationary black hole solution of a Chern-Simons model based on the semi-simple extension of the Poincar\'e gauge group is studied. The solution resembles the metric properties of the BTZ geometry but contains, in addition, non-vanishing torsion. The global structure of spacetime is characterized by three conserved charges: two associated with the mass and angular momentum and one extra constant triggered by spacetime torsion. Consequently, we show that the entropy deviates from the standard Bekenstein-Hawking value and discuss the implications of torsional charges in the context of black hole thermodynamics.

##### 5.Synchrotron emitting Komissarov torus around naked singularities

**Authors:**German D. Prada-Méndez, F. D. Lora-Clavijo, J. M. Velásquez-Cadavid

**Abstract:** From a theoretical perspective, matter accretion processes around compact objects are highly relevant as they serve as a natural laboratory to test general relativity in the strong field regime. This enables us to validate fundamental concepts such as the no-hair theorem, the cosmic censorship hypothesis, and the existence of alternative solutions to Einstein's equations that mimic the effects of black holes. In this study, we analyze the emission spectra of geometrically thick accretion disks, referred to as Polish doughnuts, around naked singularities described by the $q$-metric. To begin, we revisit the construction of equilibrium configurations of magnetized tori in this spacetime and evaluate the role of the deformation parameter over these configurations. Once we have systematically studied the disks in this spacetime, we use the \texttt{OSIRIS} code to perform a backward ray-tracing method, resulting in the first simulations of the intensity map and emission profiles of magnetized tori within this metric. Furthermore, we validate the effect of both the quadrupole moment and the angular momentum on observable quantities such as flux and intensity for optically thin and thick disks, since for values of $ q < 0$, which correspond to objects with prolate deformation, and which in turn, are constructed with higher values of angular momentum, the emission spectrum exhibits higher intensity than that obtained for Schwarzschild's spacetime. Hence, we find a first differential feature that distinguishes tori formed around naked singularities from those around static black holes.

##### 6.Testing gravity with gauge-invariant polarization states of gravitational waves

**Authors:**Márcio E. S. Alves

**Abstract:** The determination of the polarization modes of gravitational waves (GWs), and of their dispersion relations is decisive to scrutinize the viability of extended theories of gravity. A tool to investigate the polarization states of GWs is the Newman-Penrose (NP) formalism. However, if the speed of GWs is smaller than the speed of light, the number of NP variables is greater than the number of polarizations. To overpass this inconvenience we use the Bardeen formalism to describe the six possible polarization modes of GWs considering different general dispersion relations for the modes. The definition of a new gauge-invariant quantity enables an unambiguous description of the scalar longitudinal polarization mode. We apply the formalism to General Relativity, scalar-tensor theories, and $f(R)$-gravity. To obtain a bridge between theory and experiment, we derive an explicit relation between a physical observable (the derivative of the frequency shift of an electromagnetic signal) with the gauge-invariant variables. From this relation, we find an analytical formula for the Pulsar Timing rms response to each polarization mode. To estimate the sensitivity of a single Pulsar Timing we focus on the case of a dispersion relation of a massive particle. The sensitivity curves of the scalar longitudinal and vector polarization modes change significantly depending on the value of the effective mass. The detection (or absence of detection) of the polarization modes using the Pulsar Timing technique has decisive implications for alternative theories of gravity. Finally, the investigation of a cutoff frequency in the Pulsar Timing band can lead to a more stringent bound on the graviton mass than that presented by ground-based interferometers.

##### 7.Regularized Black Holes from Doubled FLRW Cosmologies

**Authors:**Marc Geiller, Etera R. Livine, Francesco Sartini

**Abstract:** Reduced general relativity for four-dimensional spherically-symmetric stationary space-times, more simply called the black hole mini-superspace, was shown in previous work to admit a symmetry under the three-dimensional Poincar\'e group ISO(2,1). Such a non-semi-simple symmetry group usually signals that the system is a special case of a more general model admitting a semi-simple Lie group symmetry. We explore here possible modifications of the Hamiltonian constraint of the mini-superspace. We identify in particular a continuous deformation of the dynamics that lifts the degeneracy of the Poincar\'e group and leads to a SO(3,1) or SO(2,2) symmetry. This deformation is not related to the cosmological constant. We show that the deformed dynamics can be represented as the superposition of two non-interacting homogeneous FRW cosmologies, with flat slices filled with perfect fluid. The resulting modified black hole metrics are found to be non-singular.

##### 1.Anisotropic Cosmology in the Local Limit of Nonlocal Gravity

**Authors:**Javad Tabatabaei, Abdolali Banihashemi, Shant Baghram, Bahram Mashhoon

**Abstract:** Within the framework of the local limit of nonlocal gravity (NLG), we investigate a class of Bianchi type I spatially homogeneous but anisotropic cosmological models. The modified field equations are presented in this case and some special solutions are discussed in detail. This modified gravity theory contains a susceptibility function S(x) such that general relativity (GR) is recovered for S = 0. In the modified anisotropic cosmological models, we explore the contribution of S(t) and its temporal derivative to the local anisotropic cosmic acceleration. The implications of our results for observational cosmology are briefly discussed.

##### 2.GRDzhadzha: A code for evolving relativistic matter on analytic metric backgrounds

**Authors:**Josu C. Aurrekoetxea, Jamie Bamber, Sam E. Brady, Katy Clough, Thomas Helfer, James Marsden, Dina Traykova, Zipeng Wang

**Abstract:** GRDzhadzha is an open-source code for relativistic simulations of matter fields on curved spacetimes that admit an analytic description (e.g. stationary black holes). It is based on the publicly available 3+1D numerical relativity code GRChombo. Such a description is valid where the density of the matter is small compared to the curvature scale of the spacetime, which is the case for many physical scenarios - for example, dark matter environments. The approach offers significant savings on memory and speed compared to running full numerical relativity simulations, since the metric variables and their derivatives are calculated analytically, and therefore are not evolved or stored on the grid. This brief paper introduces the code and gives details of some applications for which it has already been used.

##### 3.Testing general relativity via direct measurement of black hole kicks

**Authors:**Parthapratim Mahapatra, Marc Favata, K. G. Arun

**Abstract:** Asymmetric emission of gravitational waves during a compact binary coalescence results in the loss of linear momentum and a corresponding `kick' or recoil on the binary's center of mass. This leads to a direction-dependent Doppler shift of the ringdown gravitational waveform. We quantify the measurability of the kick imparted to the remnant black hole in a binary black hole merger. Future ground- and space-based gravitational wave detectors will measure this effect to within $\sim 2\%$ to $\sim 30\%$ for a subset of their expected observed sources. Certain binary configurations in the LISA band may allow a sub-percent-level measurement of this effect. This direct measurement of black hole kicks can also facilitate a novel test of general relativity based on linear momentum balance. We formulate this kick consistency test via measurement of a null variable that quantifies the difference between the inferred kick (using numerical relativity) and that observed via the Doppler-shifted ringdown signal. This null variable can be constrained (at 90% confidence) to $\sim 10\%$ to $30\%$ with Cosmic Explorer and to $\sim 3\%$ to $12\%$ with LISA.

##### 4.Constraints on charged Symmergent black hole from shadow and lensing

**Authors:**Beyhan Puliçe, Reggie C. Pantig, Ali Övgün, Durmuş Demir

**Abstract:** In this paper, we report on exact charged black hole solutions in symmergent gravity with Maxwell field. Symmergent gravity induces the gravitational constant $G$, quadratic curvature coefficient $c_{\rm O}$, and the vacuum energy $V_{\rm O}$ from the flat spacetime matter loops. In the limit in which all fields are degenerate in mass, the vacuum energy $V_{\rm O}$ can be expressed in terms of $G$ and $c_{\rm O}$. We parametrize deviation from this limit by a parameter ${\hat \alpha}$ such that the black hole spacetime is dS for ${\hat \alpha} < 1$ and AdS for ${\hat \alpha} > 1$. In our analysis, we study horizon formation, shadow cast and gravitational lensing as functions of the black hole charge, and find that there is an upper bound on the charge. At relatively low values of charge, applicable to astronomical black holes, we determine constraints on $c_{\rm O}$ and ${\hat \alpha}$ using the EHT data from Sgr. A* and M87*. We apply these constraints to reveal how the shadow radius behaves as the observer distance $r_O$ varies. It is revealed that black hole charge directly influences the shadow silhouette, but the symmergent parameters have a tenuous effect. We also explored the weak field regime by using the Gauss-Bonnet theorem to study the weak deflection angle caused by the M87* black hole. We have found that impact parameters comparable to the actual distance $D = 16.8$ Mpc show the potential detectability of such an angle through advanced astronomical telescopes. Overall, our results provide new insights into the behavior of charged black holes in the context of symmergent gravity and offer a new way to test these theories against observational data.

##### 5.Detection of Binary Black Hole Mergers from the Signal-to-Noise Ratio Time Series Using Deep Learning

**Authors:**Damon Beveridge, Linqing Wen, Andreas Wicenec

**Abstract:** Gravitational wave detection has opened up new avenues for exploring and understanding some of the fundamental principles of the universe. The optimal method for detecting modelled gravitational-wave events involves template-based matched filtering and doing a multi-detector search in the resulting signal-to-noise ratio time series. In recent years, advancements in machine learning and deep learning have led to a flurry of research into using these techniques to replace matched filtering searches and for efficient and robust parameter estimation. This paper presents a novel approach that utilizes deep learning techniques to detect gravitational waves from the signal-to-noise ratio time series produced from matched filtering. We do this to investigate if an efficient deep-learning model could replace the computationally expensive post-processing in current search pipelines. We present a feasibility study where we look to detect gravitational waves from binary black hole mergers in simulated stationary Gaussian noise from the LIGO detector in Hanford, Washington. We show that our model can match the performance of a single-detector matched filtering search and that the ranking statistic from the output of our model was robust over unseen noise, exhibiting promising results for practical online implementation in the future. We discuss the possible implications of this work and its future applications to gravitational-wave detection.

##### 1.Dark energy in conformal Killing gravity

**Authors:**Junpei Harada

**Abstract:** The Friedmann equation, enriched by an additional term that effectively takes on the role of specific dark energy, is demonstrated to serve as an exact solution within the recently proposed gravitational theory named "conformal Killing gravity". This theory does not explicitly incorporate dark energy. This finding suggests that there's no necessity to postulate the existence of dark energy as an independent physical entity. The dark energy effectively arising from this theory is characterized by a specific equation of state parameter, denoted as $\omega$, which is uniquely determined to be $-5/3$, classifying it as phantom energy. If this effective dark energy is present in a moderate amount, typically around 5\% of the total energy density at the present time, and under the assumption of density parameters for matter and the cosmological constant, $\Omega_{\rm m}\sim 0.25$ and $\Omega_\Lambda \sim 0.7$, respectively, the expansion of the universe at low redshifts ($z < 1.5$) can exceed expectations, while the expansion at $z > 1.5$ remains unchanged. This holds the potential to address the Hubble tension problem.

##### 2.Time evolution of Einstein-Maxwell-scalar black holes after a thermal quench

**Authors:**Qian Chen, Zhuan Ning, Yu Tian, Xiaoning Wu, Cheng-Yong Zhang, Hongbao Zhang

**Abstract:** We employ the holographic quench technique to drive Einstein-Maxwell-scalar (EMs) black holes out of equilibrium and study the real-time dynamics therein. From the fully nonlinear dynamical simulations, a dynamically unstable Reissner-Nordstr$\ddot{\text{o}}$m anti-de Sitter (RN-AdS) black hole can be scalarized spontaneously after an arbitrarily small quench. On the other hand, a dynamically stable scalarized black hole can be descalarized after a quench of sufficient strength. Interestingly, on the way to descalarization, the scalarized black hole behaves like a holographic superfluid, undergoing a dynamical transition from oscillatory to non-oscillatory decay. Such behaviors are related to the spectrums of quasi-normal modes of scalarized black holes, where the dominant mode migrates toward the imaginary axis with increasing quench strength. In addition, due to the $\mathbb Z_{2}$-symmetry preserved by the model, the ground state is degenerate. We find that there exists a threshold for the quench strength that induces a dynamical transition of the gravitational system from one degenerate ground state to the other. Near the threshold, the gravitational system is attracted to an excited state, that is, a RN-AdS black hole with dynamical instability.

##### 3.The doomsday of black hole evaporation

**Authors:**Shao-Jiang Wang

**Abstract:** By assuming simultaneously the unitarity of the Hawking evaporation and the universality of Bekenstein entropy bound as well as the validity of cosmic censorship conjecture, we have found that the black hole evaporation rate could evolve from the usual inverse square law in black hole mass into a constant evaporation rate near the end of the Hawking evaporation before quantum gravity could come into play, inferring a slightly longer lifetime for lighter black holes.

##### 1.Casimir wormhole with GUP correction in extended symmetric teleparallel gravity

**Authors:**Abhilipsa Sahoo, S. K. Tripathy, B. Mishra, Saibal Ray

**Abstract:** Quantum mechanical concept such as the Casimir effect is explored to model traversable wormholes in an extended teleparallel gravity theory. The minimal length concept leading to the generalized uncertainty principle (GUP) is used to obtain the Casimir energy density. The effect of the GUP correction in the geometrical and physical properties of traversable Casimir wormholes are investigated. It is noted that the GUP correction has a substantial effect on the wormhole geometry and it modifies the energy condition. From a detailed calculation of the exotic matter content of the GUP corrected Casimir wormhole, it is shown that, a minimal amount of exotic matter is sufficient to support the stability of the wormhole.

##### 2.A note on the geodesic deviation equation for null geodesics in the Schwarzschild black-hole

**Authors:**Juan J. Morales-Ruiz, Álvaro P. Raposo

**Abstract:** We use the Hamiltonian formulation of the geodesic equation in the Schwarzschild space-time so as to get the variational equation as the counterpart of the Jacobi equation in this approach. In this context we are able to apply the Morales-Ramis theorem to link the integrability of the geodesic equation to the integrability, in the sense of differential Galois theory, of the variational equation. This link is strong enough to hold even on geodesics for which the usual conserved quantities fail to be independent, as is the case of circular geodesics. We show explicitly the particular cases of some null geodesics and their variational equations.

##### 3.The Non-Relativistic Geometric Trinity of Gravity

**Authors:**William J. Wolf, James Read

**Abstract:** We complete a non-relativistic geometric trinity of gravity, by (a) taking the non-relativistic limit of the well-known geometric trinity of gravity, and (b) converting the curvature degrees of freedom of Newton-Cartan theory to purely non-metric degrees of freedom.

##### 4.Cosmological electromagnetic hopfions

**Authors:**Sergio A. Hojman, Felipe A. Asenjo

**Abstract:** It is shown that any mathematical solution for null electromagnetic field knots in flat spacetime is also a null field knotted solution for cosmological electromagnetic fields that may be obtained by replacing the time $t\rightarrow \tau=\int dt/a$, where $a=a(t)$ is the scale factor of the Universe described by the Friedman-Lema\^itre-Robertson-Walker (FLRW) cosmology, and by adequately rewriting the (empty flat spacetimes) electromagnetic fields solutions in a medium defined by the FLRW metric. We found that the dispersion (evolutoion) of electromagnetic hopfions is faster on cosmological scenarios. We discuss the implications of these results for different cosmological models.

##### 5.Charged strange star coupled to anisotropic dark energy in Tolman-Kuchowicz spacetime

**Authors:**Pramit Rej, Akashdip Karmakar

**Abstract:** The concept of dark energy can be used as a possible option to prevent the gravitational collapse of compact objects into singularities. It affects the universe on the largest scale, as it is responsible for our universe's accelerated expansion. As a consequence, it seems possible that dark energy will interact with any compact astrophysical stellar object [Phys. Rev. D 103, 084042 (2021)]. In this work, our prime focus is to develop a simplified model of a charged strange star coupled to anisotropic dark energy in Tolman-Kuchowicz spacetime (Tolman, Phys Rev 55:364, 1939; Kuchowicz, Acta Phys Pol 33:541, 1968) within the context of general relativity. To develop our model, here we consider a particular strange star object, Her X-1 with observed values of mass $=(0.85 \pm 0.15)M_{\odot}$ and radius $= 8.1_{-0.41}^{+0.41}$ km. respectively. In this context, we initially started with the equation of state (EoS) to model the dark energy, in which the dark energy density is proportional to the isotropic perfect fluid matter-energy density. The unknown constants present in the metric have been calculated by using the Darmois-Israel condition. We perform an in-depth analysis of the stability and force equilibrium of our proposed stellar configuration as well as multiple physical attributes of the model such as metric function, pressure, density, mass-radius relation, and dark energy parameters by varying dark energy coupling parameter $\alpha$. Thus after a thorough theoretical analysis, we found that our proposed model is free from any singularity and also satisfies all stability criteria to be a stable and physically realistic stellar model.

##### 6.Lyapunov Exponents to Test General Relativity

**Authors:**Alexander Deich, Nicolás Yunes, Charles Gammie

**Abstract:** Photon rings are key targets for near-future space-based very-long baseline interferometry missions. The ratio of flux measured between successive light-rings is characterized by the Lyapunov exponents of the corresponding nearly-bound null geodesics. Therefore, understanding Lyapunov exponents in this environment is of crucial importance to understanding black hole observations in general, and in particular, they may offer a route for constraining modified theories of gravity. While recent work has made significant progress in describing these geodesics for Kerr, a theory-agnostic description is complicated by the fact that Lyapunov exponents are time-parameterization dependent, which necessitates care when comparing these exponents in two different theories. In this work, we present a robust numerical framework for computing and comparing the Lyapunov exponents of null geodesics in Kerr with those in an arbitrary modified theory. We then present results obtained from calculating the Lyapunov exponents for null geodesics in two particular effective theories, scalar Gauss-Bonnet gravity and dynamical Chern-Simons gravity. Using this framework, we determine accuracy lower-bounds required before a very-long baseline interferometry observation can constrain these theories.

##### 7.Symmetric Teleparallel Gauss-Bonnet Gravity and its Extensions

**Authors:**Juan Manuel Armaleo, Sebastian Bahamonde, Georg Trenkler, Leonardo G. Trombetta

**Abstract:** General Teleparallel theories assume that curvature is vanishing in which case gravity can be solely represented by torsion and/or nonmetricity. Using differential form language, we express the Riemannian Gauss-Bonnet invariant concisely in terms of two General Teleparallel Gauss-Bonnet invariants, a bulk and a boundary one. Both terms are boundary terms in four dimensions. We also find that the split is not unique and present two possible alternatives. In the absence of nonmetricity our expressions coincide with the well-known Metric Teleparallel Gauss-Bonnet invariants for one of the splits. Next, we focus on the description where only nonmetricity is present and show some examples in different spacetimes. We finish our discussion by formulating novel modified Symmetric Teleparallel theories constructed with our new scalars.

##### 1.Holevo Cramér-Rao Bound for waveform estimation of gravitational waves

**Authors:**James W. Gardner, Tuvia Gefen, Simon A. Haine, Joseph J. Hope, Yanbei Chen

**Abstract:** Detecting kilohertz gravitational waves from the post-merger remnants of binary neutron-star mergers could enhance our understanding of extreme matter. To enable this detection, a gravitational-wave interferometer can be detuned to increase its kilohertz sensitivity. The precision limits of detuned interferometers and other cavity--based quantum sensors, however, are not well understood. The sensitivity of the standard variational readout scheme does not reach the waveform-estimation Quantum Cram\'er-Rao Bound. We establish the fundamental precision limit, the waveform-estimation Holevo Cram\'er-Rao Bound, by identifying the incompatibility of the na\"ive estimates of the signal's cosine and sine phases. For an equal weighting between the phases, we prove that the standard scheme is indeed optimal. For unequal weights, however, we propose an experimental realisation of a new measurement scheme to significantly improve the sensitivity. This scheme could facilitate kilohertz gravitational-wave astronomy and has broader applications to detuned cavity--based quantum metrology.

##### 1.Effects of coupling constants on chaos of charged particles in the $Einstein-Æ$ ther theory

**Authors:**Caiyu Liu, Xin Wu

**Abstract:** There are two free coupling parameters $c_{13}$ and $c_{14}$ in the Einstein-\AE ther metric describing a non-rotating black hole. This metric is the Reissner-Nordstr\"{o}m black hole solution when $0\leq 2c_{13}<c_{14}<2$, but it is not for $0\leq c_{14}<2c_{13}<2$. When the black hole is immersed in an external asymptotically uniform magnetic field, the Hamiltonian system describing the motion of charged particles around the black hole is not integrable. However, the Hamiltonian allows for the construction of explicit symplectic integrators. The proposed fourth-order explicit symplectic scheme is used to investigate the dynamics of charged particles because it exhibits excellent long-term performance in conserving the Hamiltonian. No universal rule can be given to the dependence of regular and chaotic dynamics on varying one or two parameters $c_{13}$ and $c_{14}$ in the two cases of $0\leq 2c_{13}<c_{14}<2$ and $0\leq c_{14}<2c_{13}<2$. The distributions of order and chaos in the binary parameter space $(c_{13},c_{14})$ rely on different combinations of the other parameters and the initial conditions.

##### 2.Bumblebee gravity with cosmological constant

**Authors:**P. Valtancoli

**Abstract:** We show how to find exact black hole solutions in bumblebee gravity with cosmological constant including BTZ black holes.

##### 3.Spinning magnetized particles orbiting magnetized Schwarzschild black holes

**Authors:**Farrux Abdulxamidov, Javlon Rayimbaev, Ahmadjon Abdujabbarov, Zdeněk Stuchlík

**Abstract:** A way to test electromagnetic field and spacetime properties around black holes is by considering the dynamics of test particles. In fact, in real astrophysical scenarios, it is hard to determine spacetime geometry which is dominating due to degeneracy gravitational effects in parameters of gravity theories. In this work, we study for the first time the dynamics of spinning particles that have magnetic dipole moments around Schwarzschild black holes immersed in an external asymptotically uniform magnetic field using the Mathisson-Papapetrou-Dixon (MPD) equation. There are two combined interactions: gravitational interaction between the spin of the particle and (electro)magnetic interaction between the external magnetic field and the magnetic dipole moment of the particle to be taken into account. First, we derive the effective potential of the test spinning magnetized particles in motion around the black hole. We also study the combined effects of spin and magnetic interactions on innermost stable circular orbits (ISCOs), the energy, and angular momentum of the particles at ISCO together with superluminal bounds. We investigated the collision of the particles and evaluated the center-of-mass energy in the collisions. Finally, we consider various cases in which neutron stars and rotating stellar mass black holes can be treated as spinning magnetized particles, evaluating the effects of the spin and magnetic moment of objects around supermassive and intermediate-mass black holes.

##### 4.Static and spherically symmetric wormholes in metric-affine theories of gravity

**Authors:**Vittorio De Falco, Salvatore Capozziello

**Abstract:** We consider static and spherically symmetric wormhole solutions in extended metric-affine theories of gravity supposing that stability and traversability of these objects can be achieved by means of the geometric degrees of freedom. In particular, we consider $f(R)$ metric, $f(T)$ teleparallel, and $f(Q)$ symmetric teleparallel models where curvature, torsion, and non-metricity rule entirely the background geometry without invoking any exotic energy-momentum tensor as matter field source. Starting from the flaring out and null energy conditions, we gather together a series of constraints which allow us to state that stable and traversable wormholes can be derived in a purely geometric approach resorting to modified gravity theories with more degrees of freedom than general relativity.

##### 5.Interacting Tachyonic Scalar Field III

**Authors:**Tanisha Joshi, S. D Pathak

**Abstract:** This study explores the plausibility of an interacting tachyonic scalar, homogeneous in nature, as a promising candidate for dynamic dark energy, offering insights into the observed accelerated expansion of the universe. The parameterization of the interaction between the tachyonic field, matter, and Hubble's parameter is performed linearly. The analysis focuses on fundamental cosmological parameters in a flat universe $(K = 0)$: expansion rate, universe age, energy density evolution for matter and the tachyonic field. The study also examines the coupling strength between the tachyonic field and matter, revealing a maximum value of unity when the interaction depends solely on their energy densities. Combining them also yields an upper limit of unity (precisely 0.7) for the coupling strength.

##### 6.Black hole surrounded by the pseudo-isothermal dark matter halo

**Authors:**Yi Yang, Dong Liu, Ali Övgün, Gaetano Lambiase, Zheng-Wen Long

**Abstract:** The abundance of dark matter in the actual universe motivates us to construct the black hole spacetime enveloped by dark matter. In this paper, we present a new spherically symmetric black hole surrounded by the pseudo-isothermal dark matter halo, and then explore the effects of the pseudo-isothermal halo profile on a rotating black hole at the M87 galactic center, aiming to achieve a black hole solution that aligns with those found in the real universe. Using the Newman-Janis method, we derive a rotating black hole solution encompassed by the pseudo-isothermal halo, which is consistent with observations of actual black holes that are believed to possess spin. Our investigation focuses on the impact of the pseudo-isothermal halo on the black hole event horizon, time-like and null orbits, as well as the black hole shadow. We find that as the spin parameter $a$ increases, the interval between the inner event horizon and the outer event horizon of the rotating black hole surrounded by the pseudo-isothermal halo in M87 diminishes. This leads to the formation of an extreme black hole. The presence of dark matter, however, has minimal effect on the event horizon. Moreover, in the M87 as the spin parameter $a$ increases, the black hole shadow deviates increasingly from a standard circle, with larger spin parameters causing more pronounced distortion relative to the standard circle. Surprisingly, we observe that the dark matter density has very little influence on the shadow of the black hole surrounded by the pseudo-isothermal halo in the M87. This study contributes to a deeper understanding of black hole structures and the role of dark matter in the universe.

##### 7.Shadow and Weak Gravitational lensing of rotating traversable Wormhole in Non-homogeneous Plasma Space-time

**Authors:**Saurabh Kumar, Akhil Uniyal, Sayan Chakrabarti

**Abstract:** In this work, we have studied the behavior of null geodesics within a rotating wormhole space-time in non-magnetized pressure-less plasma. By focusing on the dispersion relation of the plasma and disregarding its direct gravitational effects, we examine how light rays traverse in the mentioned space-time. A key highlight of the work is the necessity of a specific plasma distribution profile to establish a generalized Carter's constant, shedding light on the importance of this parameter. Furthermore, we have derived analytical formulas to distinguish the shadow boundary across various plasma profiles, uncovering a fascinating trend of diminishing shadow size as plasma density increases. Intriguingly, certain limits of the plasma parameters result in the complete disappearance of the shadow. When calculating the deflection angle by a wormhole in plasma space-time, we observe a distinct pattern: the angle decreases as the plasma parameter rises in non-homogeneous plasma space-time, diverging from the behavior observed in homogeneous plasma space-time. Also, leveraging observational data from M$87^{\ast}$, we establish constraints on the throat radius. Furthermore, minimum shadow diameters provide valuable constraints for the radial and latitudinal plasma parameters.

##### 8.Vacuum Branching, Dark Energy, Dark Matter

**Authors:**Don Weingarten

**Abstract:** Beginning with the Everett-DeWitt many-worlds interpretation of quantum mechanics, there have been a series of proposals for how the state vector of a quantum system might split at any instant into orthogonal branches, each of which exhibits approximately classical behavior. In an earlier version of the present work, we proposed a decomposition of a state vector into branches by finding the minimum of a measure of the mean squared quantum complexity of the branches in the branch decomposition. Here we define a formulation of quantum complexity for quantum electrodynamics on a lattice in Minkowski space. With respect to a particular Lorentz frame, for a system beginning in a state of low complexity, branching occurs repeatedly over time with each branch splitting successively into further sub-branches among which the branch followed by the real world is chosen according to the Born rule. Alternatively, in an explicitly Lorentz covariant formulation, the real world is a single random draw from the set of branches at asymptotically late time, which can then be restored to finite time in a particular Lorentz frame by sequentially retracing the set of branching events implied by the late time choice. The earlier version here is simplified by replacing a definition of complexity based on the physical vacuum with a definition based on the bare vacuum. As a consequence of this replacement, the physical vacuum itself is predicted to branch yielding branches with energy densities slightly larger than that of the unbranched vacuum. If the vacuum energy renormalization constant is chosen as usual to give 0 energy density to the unbranched vacuum, vacuum branches will appear to have a combination of dark energy and dark matter densities but no additional particle content.

##### 9.A Systematic Construction of Kastor-Traschen Currents and their Extensions to Generic Powers of Curvature

**Authors:**Zeynep Tugce Ozkarsligil, Bayram Tekin

**Abstract:** Kastor and Traschen constructed totally anti-symmetric conserved currents that are linear in the Riemann curvature in spacetimes admitting Killing-Yano tensors. The construction does not refer to any field equations and is built on the algebraic and differential symmetries of the Riemann tensor as well as on the Killing-Yano equation. Here we give a systematic generalization of their work and find divergence-free currents that are built from the powers of the curvature tensor. A rank-4 divergence-free tensor that is constructed from the powers of the curvature tensor plays a major role here and it comes from the Lanczos-Lovelock theory.

##### 10.Gravitational Wave Polarizations with Different Propagation Speeds

**Authors:**Kristen Schumacher, Nicolas Yunes, Kent Yagi

**Abstract:** In some modified theories of gravity, gravitational waves can contain up to six different polarizations, which can travel at speeds different from that of light. Searches for these different polarizations in gravitational wave data are important because any detection would be clear evidence of new physics, while clear non-detections could constrain some modified theories. The first step toward searching the data for such gravitational wave content is the calculation of the amplitudes of these different polarizations. Here we present a model-independent method to obtain the different polarizations of gravitational waves directly from the metric perturbation in theories where these polarizations are allowed to travel at different speeds. We develop our calculations so that the same procedure works with either the metric perturbation itself or its trace-reversed form. Our results are in agreement with previous work in the limit that all polarization speeds are the speed of light. We demonstrate how our model-independent method can be used with two specific modified theories of gravity, suggesting its wide applicability to other theories that allow for different gravitational wave propagation speeds. We further extend the ppE formalism to apply to such theories that travel with different speeds. Finally, we discuss how the different speeds of different polarizations may affect null stream tests of general relativity with gravitational wave observations by multiple interferometers. Differences in propagation speeds may make null streams ineffective or lead to the detection of what seem to be isolated scalar or vector modes.

##### 11.Leading-order corrections to the thermodynamics of Rindler modified Schwarzschild black hole

**Authors:**Surajit Mandal, Surajit Das, Ananda Pramanik, Dhruba Jyoti Gogoi

**Abstract:** In this work, we present a thermodynamical study of a Rindler modified Schwarzschild black hole under the consideration of small thermal fluctuations. In particular, we compute various stable macroscopic thermodynamic variables such as Hawking temperature, entropy, Helmholtz free energy, internal energy, enthalpy, and Gibbs free energy. To explore the effects of small statistical thermal fluctuations on stable thermodynamical parameters, we estimated the corrections to the various thermodynamical potentials of Rindler modified Schwarzschild black hole upto the first (leading) order and do a comparative study for the different values of correction parameter and Rindler acceleration parameter for fixed values of a cosmological constant. We study the stability of black holes under the consideration of thermal fluctuations and notice that the small-sized black hole is stable and the large-sized black hole is unstable for a negative value of correction parameter. For the positive value of the correction parameter, both the small and large black holes become unstable.

##### 12.Quasi-normal mode of dyonic hairy black hole and its interplay with phase transitions

**Authors:**Supragyan Priyadarshinee

**Abstract:** We study the dynamical stability of hairy dyonic black holes in the Einstein-Maxwell-scalar gravity system against the massless scalar field perturbation. We numerically obtain the corresponding quasinormal modes (QNMs) using the series solution and shooting methods for various black hole parameters. We find that the numerical values obtained from these two methods agree well with each other. The imaginary part of the QNM is always negative, indicating the stability of the dyonic hairy black hole against the scalar perturbation. We find that the decay and oscillatory modes of the scalar field perturbation increase linearly with the horizon radius for large black holes. We thoroughly investigate the behaviour of QNMs for different values of black hole parameters, including the electric charge, magnetic charge, horizon radius and hairy parameter, etc. Moreover, we also analyse the QNM near the small/large black hole phase transition and find that the nature of the QNMs is different for large and small black hole phases, suggesting QNMs as the possible probe of black hole phase transition.

##### 1.Conformal geodesics and the evolution of spacetimes with positive Cosmological constant

**Authors:**Marica Minucci

**Abstract:** This article provides a discussion on the construction of conformal Gaussian gauge systems to study the evolution of solutions to the Einstein field equations with positive Cosmological constant. This is done by means of a gauge based on the properties of conformal geodesics. The use of this gauge, combined with the extended conformal Einstein field equations, yields evolution equations in the form of a symmetric hyperbolic system for which standard Cauchy stability results can be employed. This strategy is used to study the global properties of de Sitter-like spacetimes with constant negative scalar curvature. It is then adapted to study the evolution of the Schwarzschild-de Sitter spacetime in the static region near the conformal boundary. This review is based on Class. Quantum Grav. 38 145026 and Class. Quantum Grav. 40 145005.

##### 2.On the gauge dependence of scalar induced secondary gravitational waves during radiation and matter domination eras

**Authors:**Arshad Ali, Ya-Peng Hu, Mudassar Sabir, Taotao Sui

**Abstract:** We revisit the vital issue of gauge dependence in the scalar-induced secondary gravitational waves (SIGWs), focusing on the radiation domination (RD) and matter domination (MD) eras. The energy density spectrum is the main physical observable in such induced gravitational waves. For various gauge choices, there has been a divergence in the energy density, $\Omega_{\text{GW}}$, of SIGWs. We calculate SIGWs in different gauges to quantify this divergence to address the gauge-dependent problem. In our previous studies, we had found that the energy density diverges in the polynomial power of conformal time (e.g., $\eta^6$ in uniform density gauge). We try to fix this discrepancy by adding a counter-term that removes the fictitious terms in secondary tensor perturbations. We graphically compare the calculations in various gauges and also comment on the physical origin of the observed gauge dependence.

##### 3.An ideal covariant characterization of the Kerr conformal structure

**Authors:**A. García-Parrado

**Abstract:** We present an ideal characterization of the family of four dimensional Lorentzian spacetimes that are conformally related to the Kerr vacuum solution.

##### 4.Exploring the Cosmological Model in $f(R,T^φ)$ Gravity with Observational Constraints

**Authors:**Vinod Kumar Bhardwaj, Priyanka Garg

**Abstract:** We have investigated an isotropic and homogeneous cosmological model of the universe in $f(R, T^{\phi})$ gravity, where $T^{\phi}$ is the trace of the energy-momentum tensor and $R$ is the Ricci scalar. We developed and presented exact solutions of field equations of the proposed model by taking the parametrization $q(z) =\alpha + \frac{\beta z}{1+z}$, where $\alpha$ and $\beta$ are arbitrary constants. The best possible values of the model's free parameters are estimated using the latest observational data sets of OHD, BAO, and Pantheon by applying the MCMC statistical technique. Some kinematic properties like density parameter $\rho_{\phi}$, pressure $p_{\phi}$, and equation of state parameter $\omega_{\phi}$ are derived. We have also discussed the behavior of the scalar potential $V(\phi)$ in the $f(R, T^{\phi})$ gravity theory. The behaviors of scalar fields for quintessence and phantom models are explored. Furthermore, we have discussed the behavior of energy conditions and sound speed in $f(R, T^{\phi})$ cosmology.

##### 5.Bouncing cosmology and dynamical analysis of stability with non-minimal kinetic coupled gravity

**Authors:**Alireza Amani, A. S. Kubeka, E. Mahichi

**Abstract:** In this paper, we model the bounce phase, stability and the reconstruction of the universe by non-minimal kinetic coupling. In the process, we obtained importance information about the energy density and the matter pressure of the universe in relation to the previous universe through the bounce quantum phase. The novelty of the work is that the scale factor is obtained directly from the model and is fitted with an exponential function, with this view we explore the process of the early universe even the bounce phase. After that, we plot the cosmological parameters in terms of time evolution. In what follows, we investigate the stability of the model by the dynamical system analysis in a phase plane. Finally, the phase space trajectories examine the stability of the universe, especially in the inflationary period.

##### 6.Holographic Einstein Rings of an AdS Black Hole in Massive Gravity

**Authors:**Xin-Yun Hu, M. Israr Aslam, Rabia Saleem, Xiao-Xiong Zeng

**Abstract:** In the context of holography, the Einstein ring of an AdS black hole (BH) in massive gravity (MG) is depicted. An oscillating Gaussian source on one side of the AdS boundary propagates in bulk, and we impose a response function to explain it. Using a wave optics imaging system, we obtain the optical appearance of the Einstein ring. Our research reveals that the ring can change into a luminosity-deformed ring or light spots depending on the variation of parameters and observational positions. When observers are positioned at the north pole, the holographic profiles always appear as a ring with concentric stripe surroundings, and a bright ring appears at the location of the photon sphere of the BH. These findings are consistent with the radius of the photon sphere of the BH, which is calculated in geometrical optics. Our study contributes to a better understanding of the analytical studies of holographic theory, which can be used to evaluate different types of BHs for a fixed wave source and optical system.

##### 7.Implications of a Simpson-Visser solution in Verlinde's framework

**Authors:**A. A. Araújo Filho

**Abstract:** This study focuses on investigating a regular black hole within the framework of Verlinde's emergent gravity. In particular, we explore the classical aspects of the modified Simpson--Visser solution. Our analysis reveals the presence of a unique physical event horizon. Moreover, we study the thermodynamic properties, including the \textit{Hawking} temperature, the entropy, and the heat capacity. Based on these quantities, our results show several phase transitions. Geodesic trajectories for photon--like particles, encompassing photon spheres and the formation of black hole shadows, are also calculated to comprehend the behavior of light in the vicinity of the black hole. Furthermore, we investigate the quasinormal modes using third--order WKB approximation.

##### 8.Hairy black holes, scalar charges and extended thermodynamics

**Authors:**Romina Ballestaros, Tomás Ortín

**Abstract:** We explore the use of the recently defined scalar charge which satisfies a Gauss law in stationary spacetimes, in the context of theories with a scalar potential. We find new conditions that this potential has to satisfy in order to allow for static, asymptotically-flat black-hole solutions with regular horizons and non-trivial scalar field. These conditions are equivalent to some of the known ``no-hair'' theorems (such as Bekenstein's). We study the extended thermodynamics of these systems, deriving a first law and a Smarr formula. As an example, we study the Anabal\'on-Oliva hairy black hole

##### 9.Evolution of Entropy with Cosmic Time

**Authors:**Tanisha Joshi, S. D Pathak

**Abstract:** Understanding the evolution of entropy in the universe is a fundamental aspect of cosmology. This paper investigates the evolution of entropy in a spatially flat $K=0$ universe, focusing on the contributions of matter, radiation, and dark energy components. The study derives the rate of change of entropy with respect to cosmic time, taking into account the scaling relations of energy densities and temperatures for different components. The analysis reveals the dominance of radiation entropy at early times, transitioning to matter dominance as the universe expands. The constant contribution of dark energy entropy throughout cosmic time is also considered. The paper acknowledges the limitations of the simplified model and the omission of entropy generation processes, emphasizing the importance of future research to incorporate these aspects. The results highlight the complex interplay between different components and provide insights into the dynamics of entropy in the expanding universe. This study lays the foundation for further investigations into entropy evolution, urging the consideration of more comprehensive models and numerical techniques to achieve a deeper understanding of the universe's thermodynamic behavior.

##### 10.Emergence of squeezed coherent states in Kaluza-Klein cosmology

**Authors:**A. S. Lemos, A. S. Pereira, F. A. Brito, Joao R. L. Santos

**Abstract:** In this work, we consider a propagating scalar field on Kaluza-Klein-type cosmological background. It is shown that this geometrical description of the Universe resembles - from a Hamiltonian standpoint - a damped harmonic oscillator with mass and frequency, both time-dependents. In this scenario, we construct the squeezed coherent states (SCSs) for the quantized scalar field by employing the invariant operator method of Lewis-Riesenfeld (non-Hermitian) in a non-unitary approach. The non-classicality of SCSs has been discussed by examining the quadrature squeezing properties from the uncertainty principle. Moreover, we compute the probability density, which allows us to investigate whether SCSs can be used to seek traces of extra dimensions. We then analyze the effects of the existence of supplementary space on cosmological particle production in SCSs by considering different cosmological eras.

##### 11.On the Thermodynamics of Gravitational Radiation

**Authors:**S. C. Ulhoa, F. L. Carneiro, J. W. Maluf

**Abstract:** This article deals with the thermodynamics of gravitational radiation arising from the Bondi-Sachs space-time. The equation of state found allows us to conclude that the dependence of the energy density on the temperature is a quadratic power of the latter. Such a conclusion is possible once the consequences of the first law of thermodynamics are analyzed. Then, in analogy to electromagnetic radiation, the same approach as used by Planck to obtain the quantum of energy of the gravitational radiation is proposed. An energy for the graviton proportional to the cubic frequency is found. The graviton is here understood as the quantum of gravitational energy.

##### 12.Relativistic structure of charged quark stars in energy-momentum squared gravity

**Authors:**Juan M. Z. Pretel, Takol Tangphati, Ayan Banerjee

**Abstract:** Within the context of energy-momentum squared gravity (EMSG), where non-linear matter contributions appear in the gravitational action, we derive the modified TOV equations describing the hydrostatic equilibrium of charged compact stars. We adopt two different choices for the matter Lagrangian density ($\mathcal{L}_m= p$ versus $\mathcal{L}_m= -\rho$) and investigate the impact of each one on stellar structure. Furthermore, considering a charge profile where the electric charge density $\rho_{\rm ch}$ is proportional to the standard energy density $\rho$, we solve numerically the stellar structure equations in order to obtain the mass-radius diagrams for the MIT bag model equation of state (EoS). For $\mathcal{L}_m= p$ and given a specific value of $\beta$ (including the uncharged case when $\beta= 0$), the maximum-mass values increase (decrease) substantially as the gravity model parameter $\alpha$ becomes more negative (positive). However, for uncharged configurations and considering $\mathcal{L}_m= -\rho$, our numerical results reveal that when we increase $\alpha$ (from a negative value) the maximum mass first increases and after reaching a maximum value it starts to decrease. Remarkably, this makes it a less trivial behavior than that caused by the first choice when we take into account the presence of electric charge ($\beta \neq 0$).

##### 13.Black Holes with Abelian and Non-Abelian Charges and Their Impact on Matter Accretion Flows

**Authors:**Gabriel Gómez, Ángel Rincón, Norman Cruz

**Abstract:** We study the black hole spacetime structure of a model consisting of the standard Maxwell theory and a $p$-power-Yang-Mills term. This non-linear contribution introduces a non-Abelian charge into the global solution, resulting in a modified structure of the standard Reissner-Nordstr\"{o}m black hole. Specifically, we focus on the model with $p=1/2$, which gives rise to a new type of modified Reissner-Nordstr\"{o}m black hole. For this class of black holes, we compute the event horizon, the innermost stable circular orbit, and the conditions to preserve the weak cosmic censorship conjecture. The latter condition sets a well-established relation between the electric and the Yang-Mills charges. As a first astrophysical implication, the accretion properties of spherical steady flows are investigated in detail. Extensive numerical examples of how the Yang-Mills charge affects the accretion process of an isothermal fluid in comparison to the standard Reissner-Nordstr\"{o}m and Schwarzschild black holes are displayed. Finally, analytical solutions in the fully relativistic regime, along with numerical computations, of the mass accretion rate for a polytropic fluid in terms of the electric and Yang-Mills charges are obtained. As a main result, the mass accretion rate efficiency is considerably improved, with respect to the standard Reissner-Nordstr\"{o}m and Schwarzschild solutions, for negative values of the Yang-Mills charge.

##### 1.Kerr-Newman and Electromagnetic acceleration

**Authors:**Paul H. Frampton

**Abstract:** Previous discussions of charged dark matter neglected PBH spin and employed the Reissner-Nordstrom metric. In Nature we expect the PBHs to possess spin which require use of the technically more challenging Kerr-Newman metric. It is shown that the use of K-N metric retains the principal properties already obtained using the R-N metric, in particular the dominance of Coulomb repulsion requires super-extremality and the presence of naked singularities. In this sense, the spin of the PBHs is not an essential complication.

##### 2.Aspects of Machian Gravity (I): A Mathematical Formulation for Mach's Principle

**Authors:**Santanu Das

**Abstract:** Einstein formulated the general theory of relativity (GR) with an aim to mathematically incorporate Mach's principle. Despite early hopes, it became evident that GR did not follow Mach's proposition. Nevertheless, due to its accurate explanation of various observational results, Einstein refrained from further attempts to formulate Mach's principle. Over time, multiple researchers attempted to develop gravity theories aligned with the Machian model of inertia. However, each of these theories possessed its own strengths and weaknesses. This paper presents a novel theory of gravity that fully embraces Mach's principle. This metric-based theory, termed as Machian Gravity (MG), can be derived from the action principle, ensuring compliance with all conservation laws. The theory demonstrates its efficacy by providing precise explanations for galactic rotation curves. Moreover, it effectively resolves the discrepancy between dynamic mass and photometric mass in galaxy clusters without resorting to dark matter. It also presents a resolution for the expansion history of the universe without requiring any dark matter and dark energy. Consequently, MG presents a viable and compelling alternative to the standard gravity theory.

##### 1.General spherically symmetric solution of Cotton gravity

**Authors:**Merab Gogberashvili, Ani Girgvliani

**Abstract:** In this paper we present the general spherically symmetric solution to the vacuum equations of Cotton gravity. The obtained metric solution reveals the presence of singularities at the photosphere of a spherical source, which obstruct the formation of Schwarzschild-like black holes. The solution is characterized by two integration constants that can be associated with the Hubble horizon and utilized to model the dark matter and dark energy. We examine the diverse features of the solution, including the introduction of long-range modifications to Newton's force through the incorporation of the velocity-squared repulsive term.

##### 2.The mass density contrast in perturbed Friedman-Lemaitre-Robertson-Walker cosmologies

**Authors:**Edward Malec

**Abstract:** We analyze the evolution of the mass density contrast in spherical perturbations of flat Friedman-Lemaitre-Robertson-Walker cosmologies. Both dark matter and dark energy are included. In the absence of dark energy the evolution equation coincides with that obtained by Bonnor within the ``Newtonian cosmology''.

##### 3.New perspectives on scalar fields in strong gravity

**Authors:**Georgios Antoniou

**Abstract:** Recent developments in the field of gravitational physics, including the emergence of gravitational wave astronomy, black hole images, and more accurate telescopes, have allowed us to probe the strong-field character of gravity in a novel and revolutionary manner. This accessibility related to strong gravity brings into the foreground discussions about potential modifications to General Relativity (GR) that are particularly relevant in high curvature regimes. The most straightforward way to generalise GR is to consider an additional degree of freedom, in the form of a scalar field. In this thesis, we study generalised scalar tensor theories that predict interesting strong-gravity phenomenology. First, we review scalar no-hair theorems and the conditions under which they can be evaded. Next, we study solutions of black holes with scalar hair and the way in which higher derivative terms alter their properties. We then move our discussion to the spontaneously scalarized solutions, which only deviate from GR in the strong-field regime. We propose a model consistent with compact object scalarization, that allows for a GR attractor at late times, without fine-tuning (EsRGB model). Then, we proceed to study properties of black holes and neutron stars in this theory, revealing the interesting phenomenology of the solutions. We also study the radial stability of black holes in EsRGB and perform a preliminary analysis of the hyperbolicity of the problem. Finally, we take a look at the shadows of black holes and wormholes in theories with scalar fields, in light of recent observations of black hole shadows.

##### 4.Analytical approximate solutions of AdS black holes in Einstein-Weyl-scalar gravity

**Authors:**Ming Zhang, Sheng-Yuan Li, De-Cheng Zou, Chao-Ming Zhang

**Abstract:** We consider Einstein-Weyl gravity with a minimally coupled scalar field in four dimensional spacetime. By using the Minimal Geometric Deformation (MGD) approach, we split the highly nonlinear coupled field equations into two subsystems that describing the background geometry and scalar field source, respectively. Regarding the Schwarzschild-AdS metric as a background geometry, we derive analytical approximate solutions of scalar field and deformation metric functions with Homotopy Analysis Method (HAM), providing their analytical approximations to fourth order. Moreover, we discuss the accuracy of the analytical approximations, showing they are sufficiently accurate throughout the exterior spacetime.

##### 5.Topologically Charged Rotating Wormhole

**Authors:**Faizuddin Ahmed

**Abstract:** In this paper, we present a metric ansatz represents rotating traversable wormhole named topologically charged rotating Schwarzschild-Klinkahmer wormhole space-time. We discuss geodesics motion of test particles and photon ray around this topologically charged rotating wormhole background.

##### 6.Equilibrium states from gravitational collapse of minimally coupled scalar field with non-zero potential

**Authors:**Dipanjan Dey, Koushiki, Pankaj S. Joshi

**Abstract:** We study the model of spherically symmetric and spatially homogeneous gravitational collapse of a minimally coupled scalar field. Our study focuses on obtaining the scalar field potential that leads to a final equilibrium state in the gravitational collapse. We demonstrate the existence of a class of scalar field solutions that can indeed result in such an end equilibrium state.

##### 7.The Gauss-Bonnet topological scalar in the Geometric Trinity of Gravity

**Authors:**Francesco Bajardi, Daniel Blixt, Salvatore Capozziello

**Abstract:** The Gauss-Bonnet topological scalar is presented in metric-teleparallel formalism as well as in the symmetric and general teleparallel formulations. In all of the aforementioned frameworks, the full expressions are provided explicitly in terms of torsion, non-metricity and Levi-Civita covariant derivative. The number of invariant terms of this form is counted and compared with the number which can appear in the corresponding effective field theory. Although the difference in this number is not very large, it is found that the Gauss-Bonnet invariant excludes some of the effective field theory terms. This result sheds new light on how General Relativity symmetries can be maintained at higher order in teleparallel theories: this fact appears to be highly nontrivial in the teleparallel formulation. The importance of the so-called ``pseudo-invariant'' theories like $f(T)$- and $f(T,T_\mathcal{G})$-gravity is further discussed in the context of teleparallel Gauss-Bonnet gravity.

##### 8.Modified particle lifetimes as a signature of deformed relativity

**Authors:**Pedro H. Morais, Iarley P. Lobo, Christian Pfeifer, Rafael Alves Batista, Valdir B. Bezerra

**Abstract:** We demonstrate a compatibility between the relativity principle and the clock postulate in deformed special relativity, by identifying the relevant deformed Lorentz transformations in position space between arbitrary frames. This result leads to a first-principles correction to the dilated lifetime of fundamental particles. It turns out that these modified time dilations offer a way to scrutinize Lorentz invariance (or deviations thereof) to high precision.

##### 9.Remarks on the size of apparent horizons

**Authors:**Gregory J. Galloway

**Abstract:** Marginally outer trapped surfaces (also referred to as apparent horizons) that are stable in 3-dimensional initial data sets obeying the dominant energy condition strictly are known to satisfy an area bound. The main purpose of this note is to show (in several ways) that such surfaces also satisfy a diameter bound.

##### 10.EFT corrections to scalar and vector quasinormal modes of rapidly rotating black holes

**Authors:**Filipe S. Miguel

**Abstract:** Quasinormal modes characterize the final stage of a black hole merger. In this regime, spacetime curvature is high, these modes can be used to probe potential corrections to general relativity. In this paper, we utilize the effective field theory framework to compute the leading order correction to massless scalar and electromagnetic quasinormal modes. Proceeding perturbatively in the size of the effective field theory length scale, we describe a general method to compute the frequencies for Kerr black holes of any spin. In the electromagnetic case, we study both parity even and parity odd effective field theory corrections, and, surprisingly, prove that the two have the same spectrum. Furthermore, we find that, the corrected frequencies separate into two families, corresponding to the two polarizations of light. The corrections pertaining to each family are equal and opposite. Our results are validated through several consistency checks.

##### 11.Gravitational Waves and the Galactic Potential

**Authors:**Francisco Duque

**Abstract:** Over the next decade, third-generation interferometers and the space-based LISA mission will observe binaries in galactic centers involving supermassive black holes with millions of solar masses. More precise measurements of more extreme events that probe stronger gravitational fields can have a tremendous impact on fundamental physics, astrophysics, and cosmology. However, at the galactic scale, accretion disks, dark matter halos, and dense populations of compact objects can interact gravitationally with coalescing bodies. The role these astrophysical structures play in the evolution and gravitational-wave signature of binary systems remains largely unexplored and previous studies have often relied on ad-hoc Newtonian approximations. In this thesis, we aim to improve this picture. We study how tidal deformations of matter surrounding black holes can mask off deviations from General Relativity. We also explore the deep connection between light rings -- closed orbits of massless particles -- and the proper oscillation modes of compact objects. We show that independently of the presence of an environment, the light ring controls the late-time appearance of infalling matter to distant observers and how the final black hole formed in a collision relaxes to stationarity. Finally, we develop the first fully-relativistic framework capable of studying gravitational wave emission in non-vacuum environments. We apply it to galactic black-hole binaries surrounded by a dark matter halo and observe the conversion between matter and gravitational waves. This coupling results in significant changes in the energy flux emitted, which could help constrain the properties of galactic matter distributions.

##### 12.Big-Bang is a Boundary Condition

**Authors:**Ali Kaya

**Abstract:** There is a common expectation that the big-bang singularity must be resolved in quantum gravity but it is not clear how this can be achieved. A major obstacle here is the difficulty of interpreting wave-functions in quantum gravity. The standard quantum mechanical framework requires a notion of time evolution and a proper definition of an invariant inner product having a probability interpretation, both of which are seemingly problematic in quantum gravity. We show that these two issues can actually be solved by introducing the embedding coordinates as dynamical variables \`a la Isham and Kuchar. The extended theory is identical to general relativity but has a larger group of gauge symmetries. The Wheeler-DeWitt equations describe the change of the wave-function from one arbitrary spacelike slice to another, however the constraint algebra makes this evolution purely kinematical and furthermore enforces the wave-function to be constrained in the subspace of zero-energy states. An inner product can also be introduced having all the necessary requirements. In this formalism big-bang appears as a finite field space boundary on which certain boundary conditions must be imposed for mathematical consistency. We explicitly illustrate this point both in the full theory and in the minisuperspace approximation.

##### 13.Universality in the Critical Collapse of the Einstein-Maxwell System

**Authors:**Gray D. Reid, Matthew W. Choptuik

**Abstract:** We report on critical phenomena in the gravitational collapse of the electromagnetic field in axisymmetry using cylindrical coordinates. We perform detailed numerical simulations of four families of dipole and quadrupole initial data fine-tuned to the onset of black hole formation. It has been previously observed that families which bifurcate into two on-axis critical solutions exhibit distinct growth characteristics from those which collapse at the centre of symmetry. In contrast, our results indicate similar growth characteristics and periodicity across all families of initial data, including those examined in earlier works. More precisely, for all families investigated, we observe power-law scaling for the maximum of the electromagnetic field invariant ($\mathrm{max}|F_{\mu\nu}F^{\mu\nu}| \sim |p-p^{\star}|^{-2\gamma}$) with $\gamma \approx 0.149(9)$. We find evidence of approximate discrete self-similarity in near-critical time evolutions with a log-scale echoing period of $\Delta \approx 0.62(8)$ across all families of initial data. Our methodology, while reproducing the results of prior studies up to a point, provides new insights into the later stages of critical searches and we propose a mechanism to explain the observed differences between our work and the previous calculations.

##### 14.Thin accretion disk images of the black hole in symmergent gravity

**Authors:**İlim İrfan Çimdiker, Ali Övgün, Durmuş Demir

**Abstract:** In this paper, we study circular orbits, effective potential, and thin-accretion disk of a black hole in symmergent gravity within the Novikov-Thorne model in a way including the energy flux and temperature distribution. We determine bounds on symmergent gravity parameters and conclude that the accretion disk could be used as an astrophysical tool to probe symmergent gravity.

##### 1.Existence conditions of nonsingular dyonic black holes in nonlinear electrodynamics

**Authors:**Ren Tsuda, Ryotaku Suzuki, Shinya Tomizawa

**Abstract:** General relativity coupled to nonlinear electrodynamics is known to have nonsingular black hole solutions. We investigate the existence conditions for such solutions in two-parameter Lagrangian ${\cal L} \left( {\cal F} , {\cal G} \right)$. In particular, we obtain a criterion on the Lagrangian for the existence of nonsingular black hole with a dyonic charge. In addition, we present a simple example of two-parameter Lagrangian satisfying the criterion, in which the existence of the dyonic solution is actually confirmed.

##### 2.Hamiltonian Analysis of $f(Q)$ Gravity and the Failure of the Dirac-Bergmann Algorithm for Teleparallel Theories of Gravity

**Authors:**Fabio D'Ambrosio, Lavinia Heisenberg, Stefan Zentarra

**Abstract:** In recent years, $f(Q)$ gravity has enjoyed considerable attention in the literature and important results have been obtained. However, the question of how many physical degrees of freedom the theory propagates -- and how this number may depend on the form of the function $f$ -- has not been answered satisfactorily. In this article we show that a Hamiltonian analysis based on the Dirac-Bergmann algorithm -- one of the standard methods to address this type of question -- fails. We isolate the source of the failure, show that other commonly considered teleparallel theories of gravity are affected by the same problem, and we point out that the number of degrees of freedom obtained in Phys. Rev. D 106 no. 4, (2022) by K. Hu, T. Katsuragawa, and T. Qui (namely eight), based on the Dirac-Bergmann algorithm, is wrong. Using a different approach, we show that the upper bound on the degrees of freedom is seven. Finally, we propose a more promising strategy for settling this important question.

##### 3.Image of an accreting general Ellis-Bronnikov wormhole

**Authors:**Valeria A. Ishkaeva, Sergey V. Sushkov

**Abstract:** Gravitational lensing properties of supermassive astrophysical objects, such as black holes and wormholes, provide the realistic way for their discovering and investigating. Various lensing effects in a wormhole spacetime have been widely studied in the literature. One of the most popular object for investigation is the Ellis wormhole which represents the simplest wormhole geometry. The Ellis solution represents only the particular case of a general wormhole solution found independently by Ellis and Bronnikov. Surprisingly but gravitational lensing properties of general Ellis-Bronnikov wormholes are practically not investigated. In this paper we explore in details the propagation of light, forming a shadow and silhouette, and forming an image of accretion disk in the spacetime of the Ellis-Bronnikov wormhole. As well we compare characteristics of images obtained for the Ellis-Bronnikov wormhole with those for the Schwarzschild black hole. This comparison could be useful for future observations of supermassive astrophysical objects.

##### 4.Thin accretion disk signatures in hybrid metric-Palatini f(R)-gravity

**Authors:**P. I. Dyadina, N. A. Avdeev

**Abstract:** In the present work, accretion onto a spherically symmetric black hole in the hybrid metric-Palatini f(R)-gravity is considered. The Novikov-Thorne model for a relativistic thin accretion disk is used. The energy flux, temperature distribution, emission spectrum and energy conversion efficiency of accretion disks around such black holes are numerically calculated. A comparison with the results for a Schwarzschild black hole is made and conclusions about the viability of the model are drawn. As a result, it is obtained that the accretion disks around black holes in hybrid metric-Palatini f(R)-gravity are colder and less luminous than in general relativity.

##### 5.Global dynamics of two models for Quintom Friedman-Lemaître-Robertson-Walker Universes

**Authors:**Genly Leon
Catolica del Norte U. and DUT, Durban, Alan Coley
Dalhousie U., Andronikos Paliathanasis
DUT, Durban and Catolica del Norte U., Jonathan Tot
Dalhousie U., Balkar Yildirim
Dalhousie U.

**Abstract:** We comprehensively analyze the dynamics for the gravitational field equations for the Chiral-Quintom theory in a Friedman-Lema\^itre-Robertson-Walker cosmology with an additional matter source. We consider a new set of dimensionless variables and write the field equations in the equivalent form of an algebraic-differential system. Specifically, we consider two families of quintom models where the two scalar fields interact in the kinetic sector. We mathematically focus on the dynamical effect of spatial curvature. Physically, we find two periods of inflation related to the Universe's early and late-time acceleration phases.

##### 1.Quasinormal modes of the spherical bumblebee black holes with a global monopole

**Authors:**Rui-Hui Lin, Rui Jiang, Xiang-Hua Zhai

**Abstract:** The bumblebee model is an extension of the Einstein-Maxwell theory that allows for the spontaneous breaking of the Lorentz symmetry of the spacetime. In this paper, we study the quasinormal modes of the spherical black holes in this model that are characterized by a global monopole. We analyze the two cases with a vanishing cosmological constant or a negative one (the anti-de Sitter case). We find that the black holes are stable under the perturbation of a massless scalar field. However, both the Lorentz symmetry breaking and the global monopole have notable impacts on the evolution of the perturbation. The Lorentz symmetry breaking may prolong or shorten the decay of the perturbation according to the sign of the breaking parameter. The global monopole, on the other hand, has different effects depending on whether a nonzero cosmological constant presences: it reduces the damping of the perturbations for the case with a vanishing cosmological constant, but has little influence for the anti-de Sitter case.

##### 2.Gravitational Wave Heating

**Authors:**Vishnu Kakkat, Nigel T. Bishop, Amos S. Kubeka

**Abstract:** It was shown in previous work that when a gravitational wave (GW) passes through a viscous shell of matter the magnitude of the GW will be damped and there are astrohysical circumstances in which the damping is almost complete. The energy transfer from the GWs to the fluid will increase its temperature. We construct a model for this process and obtain an expression for the temperature distribution inside the shell in terms of spherical harmonics. Further, it is shown that this effect is astrophysically significant: a model problem is constructed for which the temperature increase is of order $10^7{}^\circ$K.

##### 3.How well can modified gravitational wave propagation be constrained with strong lensing?

**Authors:**Harsh Narola, Justin Janquart, Leïla Haegel, K. Haris, Otto A. Hannuksela, Chris Van Den Broeck

**Abstract:** Strong gravitational lensing produces multiple images of a gravitational wave (GW) signal, which can be observed by detectors as time-separated copies of the same event. It has been shown that under favourable circumstances, by combining information from a quadruply lensed GW with electromagnetic observations of lensed galaxies, it is possible to identify the host galaxy of a binary black hole coalescence. Comparing the luminosity distance obtained through electromagnetic means with the effective luminosity distance inferred from the lensed GW signal would then enable us to constrain alternative theories of gravity that allow for modified GW propagation. Here we analyze models including large extra spatial dimensions, a running Planck mass, and a model that captures propagation effects occurring in a variety of alternative theories to general relativity. We consider a plausible population of lenses and binary black holes and use Bayesian inference on simulated GW signals as seen in current detectors at design sensitivity, to arrive at a realistic assessment of the bounds that could be placed. We find that, due to the fact that the sources of lensed events will typically be at much larger redshifts, this method can improve over bounds from GW170817 and its electromagnetic counterpart by a factor of $\sim 5$ to $\mathcal{O}(10^2)$, depending on the alternative gravity model.

##### 4.Tadpole Cosmology: Milne Solution as a Cosmological Constant Hideout

**Authors:**Stephen Appleby, Reginald Christian Bernardo

**Abstract:** Dynamical cancellation frameworks present a potential means of mitigating the effect of a large vacuum energy, that would otherwise ruin the late-time, low energy dynamics of the Universe. Certain models in the literature, such as the Fab Four and Well Tempering, realize this idea by introducing some degeneracy in the dynamical equations. In this paper, we introduce a third potential route to self-tuning, and infer the existence of a new, exact Milne solution in the simplest tadpole plus cubic-Galileon scalar-tensor theory. We study the dynamics of the scalar field and metric in the vicinity of the Milne coordinate singularity, and find that the vacuum solution belongs to a more general family of Milne-like metrics. By numerically evolving the field equations for a range of initial conditions, we show that the Milne solution is not an attractor, and varying the initial scalar field data can lead to completely different asymptotic states; exponential growth of the scale factor, a static non-spatially flat metric or a severe finite-time instability in the scalar field and metric. We generalise the Milne solution to a class of FLRW spacetimes, finding that the tadpole-cubic Galileon model admits perfect-fluid-like solutions in the presence of matter. Finally, we present a second Horndeski model which also admits an exact Milne solution, hinting at the existence of a larger undiscovered model space containing vacuum-energy-screened solutions.

##### 5.A new 2D limit of general relativity

**Authors:**Christian G. Boehmer, Erik Jensko

**Abstract:** It is well known that the Einstein-Hilbert action in two dimensions is topological and yields an identically vanishing Einstein tensor. Consequently one is faced with difficulties when formulating a non-trivial gravity model. We present a new, intrinsically two-dimensional, approach to this problem based on the Einstein action. This yields a well defined variational approach which results in new field equations that break diffeomorphism invariance. Our proposed approach does not require the introduction of additional scalar fields, nor the use of conformal transformations. However, we can show how including conformal counter terms leads to equivalent results. In doing so, we can provide an explanation for why previous approaches worked. Solutions to the field equations are briefly discussed.

##### 6.Earthquakes as probing tools for gravity theories

**Authors:**Aleksander Kozak, Aneta Wojnar

**Abstract:** We propose a novel method for testing gravity models using seismic data from Earth. By imposing observational constraints on Earth's moment of inertia and mass, we rigorously limit the gravitational models' parameters within a $2\sigma$ accuracy. Our method constrains the parameters governing additional terms to the General Relativity Lagrangian to the following ranges: $-2\times10^9\lesssim\beta\lesssim 10^9 \text{m}^2$ for Palatini $f(R)$ gravity, $-8\times10^9\lesssim\epsilon\lesssim 4\times 10^9 \text{m}^2$ for Eddington-inspired Born-Infeld gravity, and $-10^{-3}\lesssim\Upsilon\lesssim10^{-3}$ for Degenerate Higher-Order Scalar-Tensor theories. We also discuss potential avenues to enhance the proposed method, aiming to impose even tighter constraints on gravity models.

##### 7.Formulation Improvements for Critical Collapse Simulations

**Authors:**Daniela Cors, Sarah Renkhoff, Hannes R. Rüter, David Hilditch, Bernd Brügmann

**Abstract:** The precise tuning required to observe critical phenomena in gravitational collapse poses a challenge for most numerical codes. First, threshold estimation searches may be obstructed by the appearance of coordinate singularities, indicating the need for a better gauge choice. Second, the constraint violations to which simulations are susceptible may be too large and force searches to terminate prematurely. This is a particularly serious issue for first order formulations. We want our adaptive pseudospectral code bamps to be a robust tool for the study of critical phenomena so, having encountered both of these difficulties in work on the vacuum setting, we turn here to investigate these issues in the classic context of a spherically symmetric massless scalar field. We suggest two general improvements. We propose a necessary condition for a gauge choice to respect discrete self-similarity (DSS). The condition is not restricted to spherical symmetry and could be verified with any 3+1 formulation. After evaluating common gauge choices against this condition, we suggest a DSS-compatible gauge source function in generalized harmonic gauge (GHG). To control constraint violations, we modify the constraint damping parameters of GHG, adapting them to collapse spacetimes. This allows us to improve our tuning of the critical amplitude for several families of initial data, even going from 6 up to 11 digits. This is the most precise tuning achieved with the first order GHG formulation to date. Consequently, we are able to reproduce the well known critical phenomena as well as competing formulations and methods, clearly observing up to 3 echoes.

##### 8.Interior spacetimes sourced by stationary differentially rotating irrotational cylindrical fluids. IV. Radial pressure

**Authors:**M. -N. Célérier

**Abstract:** In a recent series of papers new exact analytical solutions of the field equations of General Relativity representing interior spacetimes sourced by stationary rigidly rotating cylinders of fluids with various equations of state have been displayed. This work is currently extended to the cases of differentially rotating irrotational fluids. The results are presented in a new series of papers considering, in turn, a perfect fluid source, as well as the three anisotropic pressure cases already studied in the rigidly rotating configuration. Here, we analyze the case of a fluid with radially directed pressure. Four classes of solutions are identified from the field equations. Among them, class I and III are fully integrated, and their mathematical and physical properties are studied, which implies a ruling out of class III for lack of proper metric signature. For each of the two other classes, a set of simplified differential equation is displayed so as to ease their possible further numerical integration. Finally, a comparison with the corresponding rigidly rotating fluid solution is provided.

##### 1.Accretion Disk for regular black holes with sub-Planckian curvature

**Authors:**Wei Zeng, Yi Ling, Qing-Quan Jiang, Guo-Ping Li

**Abstract:** We investigate the accretion disk for a sort of regular black holes which are characterized by sub-Planckian curvature and Minkowskian core. We derive null geodesics outside the horizon of such regular black holes and analyze the feature of the light rays from the accretion disk which can be classified into direct emission, lensed rings, and photon rings. We find that the observed brightness under different emission models is mainly determined by direct emission, while the contribution from the flux of the lensed and photon rings is limited. By comparing with Bardeen black hole with a dS core, it is found that the black hole with a Minkowskian core exhibits distinct astronomical optical features when surrounded by accretion disk, which potentially provides a way to distinguish these two sorts of black holes by astronomical observation.

##### 2.Model-agnostic search for the quasinormal modes of gravitational wave echoes

**Authors:**Di Wu, Pengyuan Gao, Jing Ren, Niayesh Afshordi

**Abstract:** Post-merger gravitational wave echoes provide a unique opportunity to probe the near-horizon structure of astrophysical black holes, that may be modified due to non-perturbative quantum gravity phenomena. However, since the waveform is subject to large theoretical uncertainties, it is necessary to develop model-agnostic search methods for detecting echoes from observational data. A promising strategy is to identify the characteristic quasinormal modes (QNMs) associated with echoes, {\it in frequency space}, which complements existing searches of quasiperiodic pulses in time. In this study, we build upon our previous work targeting these modes by incorporating relative phase information to optimize the Bayesian search algorithm. Using a new phase-marginalized likelihood, the performance can be significantly improved for well-resolved QNMs. This enables an efficient model-agnostic search for QNMs of different shapes by using a simple search template. To demonstrate the robustness of the search algorithm, we construct four complementary benchmarks for the echo waveform that span a diverse range of different theoretical possibilities for the near-horizon structure. We then validate our Bayesian search algorithms by injecting the benchmark models into different realizations of Gaussian noise. Using two types of phase-marginalized likelihoods, we find that the search algorithm can efficiently detect the corresponding QNMs. Therefore, our search strategy provides a concrete Bayesian and model-agnostic approach to "quantum black hole seismology".

##### 3.Impact of the noise knowledge uncertainty for the science exploitation of cosmological and astrophysical stochastic gravitational wave background with LISA

**Authors:**Martina Muratore, Jonathan Gair, Lorenzo Speri

**Abstract:** This paper investigates the impact of a lack of knowledge of the instrumental noise on the characterisation of stochastic gravitational wave backgrounds with the Laser Interferometer Space Antenna (LISA). We focus on constraints on modelled backgrounds that represent the possible backgrounds from the mergers of binary black holes of stellar origin, from primordial black hole generation, from non-standard inflation, and from sound wave production during cosmic fluid phase transitions. We use splines to model generic, slowly varying, uncertainties in the auto and cross-spectral densities of the LISA time delay interferometry channels. We find that allowing for noise knowledge uncertainty in this way leads to one to two orders of magnitude degradation in our ability to constrain stochastic backgrounds, and a corresponding increase in the background energy density required for a confident detection. We also find that to avoid this degradation, the LISA noise would have to be known at the sub-percent level, which is unlikely to be achievable in practice.

##### 4.Black hole solutions to Einstein-Bel-Robinson gravity

**Authors:**S. N. Sajadi, Robert B. Mann, H. Sheikhahmadi, M. Khademi

**Abstract:** By employing a combination of perturbative analytic methods, we study the physical properties of a static-spherically symmetric black hole in the framework of the recently proposed Einstien-Bel-Robinson version of gravity. We show that interestingly the theory propagates a transverse and massive graviton on a maximally symmetric background with positive energy. There is also a single ghost-free branch that returns to the Einstein case when \beta\to 0. Then, we obtain the conserved charges of the theory to study the thermodynamics of the black hole solutions. We get the thermodynamical quantities and show that the solutions undergo a first-order phase transition with associated Van der Waals behavior. We analyze the specific heat, determining that the black holes are thermodynamically stable over large regions of parametric space.

##### 5.Black hole thermodynamics in Horndeski theories

**Authors:**Masato Minamitsuji, Kei-ichi Maeda

**Abstract:** We investigate thermodynamics of static and spherically symmetric black holes (BHs) in the Horndeski theories. Because of the presence of the higher-derivative interactions and the nonminimal derivative couplings of the scalar field, the standard Wald entropy formula may not be directly applicable. Hence, following the original formulation by Iyer and Wald, we obtain the differentials of the BH entropy and the total mass of the system in the Horndeski theories, which lead to the first-law of thermodynamics via the conservation of the Hamiltonian. Our formulation covers the case of the static and spherically symmetric BH solutions with the static scalar field and those with the linearly time-dependent scalar field in the shift-symmetric Horndeski theories. We then apply our results to explicit BH solutions in the Horndeski theories. In the case of the conventional scalar-tensor theories and the Einstein-scalar-Gauss-Bonnet theories, we recover the BH entropy obtained by the Wald entropy formula. In the shift-symmetric theories, in the case of the BH solutions with the the static scalar field we show that the BH entropy follows the ordinary area law even in the presence of the nontrivial profile of the scalar field. On the other hand, in the case of the BH solutions where the scalar field linearly depends on time, i.e., the stealth Schwarzschild and Schwarzschild-(anti-) de Sitter solutions, the BH entropy also depends on the profile of the scalar field. By use of the entropy, we find that there exists some range of the parameters in which Schwarzschild$-$(AdS) BH with non-trivial scalar field is thermodynamically stable than Schwarzschild$-$(AdS) BH without scalar field in general relativity.

##### 6.Gravitationally induced matter creation and cosmological consequences

**Authors:**Trishit Banerjee, Goutam Mandal, Atreyee Biswas, Sujay Kr. Biswas

**Abstract:** In this work, a two-fluid interacting model in a flat FLRW universe has been studied considering particle creation mechanism with a particular form of particle creation rate $\Gamma=\Gamma_0 H+\frac{\Gamma_1}{H}$ from different aspects. Statistical analysis with a combined data set of SNe Ia (Supernovae Type Ia) and Hubble data is performed to achieve the best-fit values of the model parameters, and the model is compatible with current observational data. We also perform a dynamical analysis of this model to get an overall qualitative description of the cosmological evolution by converting the governing equations into a system of ordinary differential equations considering a proper transformation of variables. We find some non-isolated sets of critical points, among which some usually are normally hyperbolic sets of points that describe the present acceleration of the Universe dominated by dark energy mimicking cosmological constant or phantom fluid. Scaling solutions are also obtained from this analysis, and they can alleviate the coincidence problem successfully. Finally, the thermodynamic analysis shows that the Generalized second law of thermodynamics is valid in an irreversible thermodynamic context.

##### 7.Hamiltonian formulation of gravity as a spontaneously-broken gauge theory of the Lorentz group

**Authors:**Mehraveh Nikjoo, Tom Zlosnik

**Abstract:** A number of approaches to gravitation have much in common with the gauge theories of the standard model of particle physics. In this paper, we develop the Hamiltonian formulation of a class of gravitational theories that may be regarded as spontaneously-broken gauge theories of the complexified Lorentz group $SO(1,3)_C$ with the gravitational field described entirely by a gauge field valued in the Lie algebra of $SO(1,3)_C$ and a `Higgs field' valued in the group's fundamental representation. The theories have one free parameter $\beta$ which appears in a similar role to the inverse of the Barbero-Immirzi parameter of Einstein-Cartan theory. However, contrary to that parameter, it is shown that the number of degrees of freedom crucially depends on the value of $\beta$. For non-zero values of $\beta$, it is shown that three complex degrees of freedom propagate on general backgrounds, and for the specific values $\beta=\pm i$ an extension to General Relativity is recovered in a symmetry-broken regime. For the value $\beta=0$, the theory propagates no local degrees of freedom. A non-zero value of $\beta$ corresponds to the self-dual and anti-self-dual gauge fields appearing asymmetrically in the action, therefore in these models, the existence of gravitational degrees of freedom is tied to chiral asymmetry in the gravitational sector.

##### 8.Detecting Dark Domain Walls

**Authors:**Kate Clements, Benjamin Elder, Lucia Hackermueller, Mark Fromhold, Clare Burrage

**Abstract:** Light scalar fields, with double well potentials and direct matter couplings, undergo density driven phase transitions, leading to the formation of domain walls. Such theories could explain dark energy, dark matter or source the nanoHz gravitational-wave background. We describe an experiment that could be used to detect such domain walls in a laboratory experiment, solving for the scalar field profile, and showing how the domain wall affects the motion of a test particle. We find that, in currently unconstrained regions of parameter space, the domain walls leave detectable signatures.

##### 9.Bogoliubov Transformation and Schrodinger Representation on Curved Space

**Authors:**Musfar Muhamed Kozhikkal, Arif Mohd

**Abstract:** It is usually accepted that quantum dynamics described by Schrodinger equation that determines the evolution of states from one Cauchy surface to another is unitary. However, it has been known for some time that this expectation is not borne out in the conventional setting in which one envisages the dynamics on a fixed Hilbert space. Indeed it is not even true for linear quantum field theory on Minkowski space if the chosen Cauchy surfaces are not preserved by the flow of a timelike Killing vector. This issue was elegantly addressed and resolved by Agullo and Ashtekar who showed that in a general setting quantum dynamics in the Schrodinger picture does not take place in a fixed Hilbert space. Instead, it takes place on a non-trivial bundle over time, the Hilbert bundle, whose fibre at a given time is a Hilbert space at that time. In this article, we postulate a Schrodinger equation that incorporates the effect of change in vacuum during time evolution by including the Bogoliubov transformation explicitly in the Schrodinger equation. More precisely, for a linear (real) Klein-Gordon field on a globally hyperbolic spacetime we write down a Schrodinger equation that propagates states between arbitrary chosen Cauchy surfaces, thus describing the quantum dynamics on a Hilbert bundle. We show that this dynamics is unitary if a specific tensor on the canonical phase space satisfies the Hilbert-Schmidt condition. Generalized unitarity condition of Agullo-Ashtekar follows quite naturally from our construction.

##### 10.Alleviating both $H_0$ and $σ_8$ tensions in Tsallis cosmology

**Authors:**Spyros Basilakos, Andreas Lymperis, Maria Petronikolou, Emmanuel N. Saridakis

**Abstract:** We present how Tsallis cosmology can alleviate both $H_0$ and $\sigma_8$ tensions simultaneously. Such a modified cosmological scenario is obtained by the application of the gravity-thermodynamics conjecture, but using the non-additive Tsallis entropy, instead of the standard Bekenstein-Hawking one. Hence, one obtains modified Friedmann equations, with extra terms that depend on the new Tsallis exponent $\delta$ that quantifies the departure from standard entropy. We show that for particular $\delta$ choices we can obtain a phantom effective dark energy, which is known to be one of the sufficient mechanisms that can alleviate $H_0$ tension. Additionally, for the same parameter choice we obtain an increased friction term and an effective Newton's constant smaller than the usual one, and thus the $\sigma_8$ tension is also solved. These features act as a significant advantage of Tsallis modified cosmology.

##### 11.Swampland criteria and neutrino generation in a non-cold dark matter universe

**Authors:**Martiros Khurshudyan

**Abstract:** In this paper, the implications of string Swampland criteria for a dark energy-dominated universe, where we have a deviation from the cold dark matter model, will be discussed. In particular, we have considered two models. One of them is one parameter model, while the second one has been crafted to reveal the dynamics in the deviation. The analysis has been obtained through the use of Gaussian processes (GPs) and $H(z)$ expansion rate data (a $30$-point sample deduced from a differential age method and a $10$-point sample obtained from the radial BAO method). We learned that the tension with the Swampland criteria still will survive as in the cases of the models where dark matter is cold. In the analysis besides mentioned $40$-point $H(z)$ data, we used the latest values of $H_{0}$ reported by the Planck and Hubble missions to reveal possible solutions for the $H_{0}$ tension problem. Finally, the constraints on the neutrino generation number have been obtained revealing interesting results to be discussed yet. This and various related questions have been left to be discussed in forthcoming papers.

##### 12.Quasinormal modes of the Schwarzchild black hole with a deficit solid angle and quintessence-like matter: Scalar and electromagnetic perturbations

**Authors:**L. A. López, Omar Pedraza

**Abstract:** We study the quasinormal modes (QNM) for scalar, and electromagnetic perturbations in the Schwarzchild black hole with a deficit solid angle and quintessence-like matter. Using the sixth--order WKB approximation and the improved asymptotic iteration method (AIM) we can determine the dependence of the quasinormal modes on the parameters of the black hole and the parameters on the test fields. The values of the real part and imaginary parts of the quasi--normal modes increase with the decrease of the values of the deficit solid angle and density of quintessence-like matter. The quasinormal modes gotten by these two methods are in good agreement. Using the finite difference method, we obtain the time evolution profile of such perturbations in this Black Hole.

##### 13.Shadows near supermassive black holes: from a theoretical concept to GR test

**Authors:**Alexander F. Zakharov

**Abstract:** General relativity (GR) passed many astronomical tests but in majority of them GR predictions have been tested in a weak gravitational field approximation. Around 50 years ago a shadow has been introduced by J. Bardeen as a purely theoretical concept but due to an enormous progress in observational and computational facilities this theoretical prediction has been confirmed and the most solid argument for an existence of supermassive black holes in Sgr A* and M87* has been obtained.

##### 14.Constraining the nature of dark compact objects with spin-induced octupole moment measurement

**Authors:**Pankaj Saini, N. V. Krishnendu

**Abstract:** Various theoretical models predict the existence of exotic compact objects that can mimic the properties of black holes (BHs). Gravitational waves (GWs) from the mergers of compact objects have the potential to distinguish between exotic compact objects and BHs. The measurement of spin-induced multipole moments of compact objects in binaries provides a unique way to test the nature of compact objects. The observations of GWs by LIGO and Virgo have already put constraints on the spin-induced quadrupole moment, the leading order spin-induced moment. In this work, we develop a Bayesian framework to measure the spin-induced octupole moment, the next-to-leading order spin-induced moment. The precise measurement of the spin-induced octupole moment will allow us to test its consistency with that of Kerr BHs in general relativity and constrain the allowed parameter space for non-BH compact objects. For various simulated compact object binaries, we explore the ability of the LIGO and Virgo detector network to constrain spin-induced octupole moment of compact objects. We find that LIGO and Virgo at design sensitivity can constrain the symmetric combination of component spin-induced octupole moments of binary for dimensionless spin magnitudes $\sim 0.8$. Further, we study the possibility of simultaneously measuring the spin-induced quadrupole and octupole moments. Finally, we perform this test on selected GW events reported in the third GW catalog. These are the first constraints on spin-induced octupole moment using full Bayesian analysis.

##### 15.Lorentzian Robin Universe

**Authors:**Manishankar Ailiga, Shubhashis Mallik, Gaurav Narain

**Abstract:** In this paper, we delve into the gravitational path-integral of Gauss-Bonnet gravity in four spacetime dimensions, in the mini-superspace approximation. Our primary focus lies in. investigating the transition amplitude between distinct boundary configurations. Of particular interest is the case of Robin boundary conditions, known to lead to a stable Universe in Einstein-Hilbert gravity, alongside Neumann boundary conditions. To ensure a consistent variational problem, we supplement the bulk action with suitable surface terms. This study leads us to compute the necessary surface terms required for Gauss-Bonnet gravity with the Robin boundary condition, which wasn't known earlier. Thereafter, we perform an exact computation of the transition amplitude. Through $\hbar\to0$ analysis, we discover that Gauss-Bonnet gravity inherently favors the initial configuration, aligning with the Hartle-Hawking no-boundary proposal. Remarkably, as the Universe expands, it undergoes a transition from the Euclidean (imaginary time) to the Lorentzian phase (real time). To further reinforce our findings, we employ a saddle point analysis utilizing the Picard-Lefschetz methods. The saddle point analysis allows us to find the boundary configurations which lead to Hartle-Hawking no-boundary Universe that agrees with the exact computations.

##### 1.Non-perturbative stabilization of two Kähler moduli in type-IIB/F theory and the inflaton potential

**Authors:**Abhijit Let, Arunoday Sarkar, Chitrak Sarkar, Buddhadeb Ghosh

**Abstract:** We consider a combination of perturbative and non-perturbative corrections in K\"ahler moduli stabilizations in the configuration of three magnetised intersecting D7 branes in the type-IIB/F theory, compactified on the 6d T^6/Z_N orbifold of Calabi-Yau three-fold (CY_3). Two of the K\"ahler moduli are stabilized non-perturbatively, out of the three which get perturbative corrections up to one-loop-order multi-graviton scattering amplitudes in the large volume scenario. In this framework, the dS vacua are achieved through all K\"ahler moduli stabilizations by considering the D-term. We obtain inflaton potentials of slow-roll plateau-type, which are expected by recent cosmological observations. Calculations of cosmological parameters with the potentials yield experimentally favoured values.

##### 2.Thermodynamics and evaporation of perfect fluid dark matter black hole in phantom background

**Authors:**Xiao Liang, Ya-Peng Hu, Chen-Hao Wu, Yu-Sen An

**Abstract:** We present a novel interpretation of the thermodynamics of perfect fluid dark matter (PFDM) black hole based on Misner-Sharp energy, and then investigate its evaporation behavior. We find that the ratio between dark sector initial density and black hole horizon radius significantly influences black hole evaporation behaviors. We demonstrate that the presence of the dark sector can significantly extend the lifetime of a black hole which is similar to the Reissner-Nordstrom case. Our work reformulates the thermodynamics of PFDM black holes and points out the existence of long-lived black holes in the presence of the dark sector.

##### 3.Reconstruction of relativistic modified Newtonian dynamics for various cosmological scenarios

**Authors:**Qi-Ming Fu, Meng-Ci He, Tao-Tao Sui, Xin Zhang

**Abstract:** In this paper, we present several explicit reconstructions for a novel relativistic theory of modified Newtonian dynamics (RMOND) derived from the background of Friedmann-Lema$\hat{\text{\i}}$tre-Robertson-Walker cosmological evolution. It is shown that the Einstein-Hilbert Lagrangian with a positive cosmological constant is the only Lagrangian capable of accurately replicating the exact expansion history of the $\Lambda$ cold dark matter ($\Lambda$CDM) universe filled solely with dust-like matter and the only way to achieve this expansion history for the RMOND theory is to introduce additional degrees of freedom to the matter sectors. Besides, we find that the $\Lambda$CDM-era also can be replicated without any real matter field within the framework of the RMOND theory and the cosmic evolution exhibited by both the power-law and de-Sitter solutions also can be obtained.

##### 4.Cosmic time and the initial state of the universe

**Authors:**Chopin Soo

**Abstract:** Exact solution of the Hamiltonian constraint in canonical gravity and the resultant reduction of Einstein's theory reveal the synergy between gravitation and the cosmic clock of our expanding universe. In conjunction with a paradigm shift from four-covariance to just spatial diffeomorphism invariance, causal time-ordering of the quantum state of the universe and its evolution in cosmic time become meaningful. This advocated framework prompts natural extensions. A salient feature is the addition of a Cotton-York term to the physical Hamiltonian. This radically changes the solution to the initial data problem and the quantum origin of the universe. It lends support to the quantum beginning of the universe as an exact Chern-Simons Hartle-Hawking state that features Euclidean-Lorentzian instanton tunneling. A signature of this state is that it manifests, at the lowest order approximation, scale-invariant two-point correlation function for transverse traceless quantum metric fluctuations. This initial quantum state also yields, at the level of expectation values, a low-entropy hot smooth Robertson-Walker beginning that is in accord with Penrose's Weyl Curvature Hypothesis. Consequently, the gravitational arrow of time of increasing spatial volume and the thermodynamic Second Law arrow of time of increasing entropy concur as our universe expands and ages.

##### 5.Gravito-electromagnetic equivalence on large scales

**Authors:**Panagiotis Mavrogiannis

**Abstract:** We revisit the relativistic coupling between gravity and electromagnetism, putting particularly into question the status of the latter on large scales; whether it behaves as a source or as a form of gravity. Considering a metric-affine framework and a simple action principle, we find out that a component of gravity, the so-called homothetic curvature field (associated with length changes), satisfies both sets of Maxwell equations. Therefore, we arrive at a gravito-electromagnetic equivalence analogous to the mass-energy equivalence. We raise and discuss some crucial questions implied by the aforementioned finding concerning the status of electromagnetism on large scales.

##### 6.Thermodynamics of Kerr-Sen-AdS black holes in the restricted phase space

**Authors:**Md Sabir Ali, Sushant G. Ghosh, Anzhong Wang

**Abstract:** We analyse the restricted phase space thermodynamics (RPST) of Kerr-Sen-AdS black holes with the central charge $C$ and its conjugate chemical potential $\mu$ but exclude the familiar $PdV$ term in the first law of black hole thermodynamics. That gives rise to a new perspective on the thermodynamics of black holes. Using the scaling properties, we investigate the first law and the corresponding Euler formula. Such formalism has its beauty, to say, for example, the mass is considered to be a homogeneous function of the extensive variables in the first order. In contrast, the intensive variables are of zeroth order. Because of the complicated expressions of the metric, we numerically calculate the critical values of the thermodynamic quantities. We find the phase transition behaviour of the free energy and other thermodynamic conjugate variables that appear in the first law. The RPST of the Kerr-Sen-AdS black holes is like that of the Reissner-Nordstr$\ddot{o}$m-AdS and the Kerr-AdS black holes. Such notions of the phase transition behaviour show that there should be some underlying universality in the RPST formalism.

##### 7.Compact stars in $f(T) = T +ξT^β$ gravity

**Authors:**José C. N. de Araujo, Hemily G. M. Fortes

**Abstract:** The Teleparallel Theory is equivalent to General Relativity, but whereas in the latter gravity has do with curvature, in the former gravity is described by torsion. As is well known, there is in the literature a host of alternative theories of gravity, among them the so called extended theories, in which additional terms are added to the action, such as for example in the $f(R)$ and $f(T)$ gravities, where $R$ is the Ricci scalar and $T$ is the scalar torsion, respectively. One of the ways to probe alternative gravity is via compact objects. In fact, there is in the literature a series of papers on compact objects in $f(R)$ and $f(T)$ gravity. In particular, there are several papers that consider $f(T) = T + \xi T^2$, where $\xi$ is a real constant. In this paper, we generalise such extension considering compact stars in $f (T ) = T + \xi T^\beta$ gravity, where $\xi$ and $\beta$ are real constants} {and looking out for the implications in their maximum masses and compactness in comparison to the General Relativity.

##### 8.Cosmology in gravity models with broken diffeomorphisms

**Authors:**Antonio G. Bello-Morales, Antonio L. Maroto

**Abstract:** We study the cosmological implications of gravity models which break diffeomorphisms (Diff) invariance down to transverse diffeomorphisms (TDiff). We start from the most general gravitational action involving up to quadratic terms in derivatives of the metric tensor and identify TDiff models as the only stable theories consistent with local gravity tests. These models propagate an additional scalar graviton and although they are indistinguishable from GR at the post-Newtonian level, their cosmological dynamics exhibits a rich phenomenology. Thus we show that the model includes standard $\Lambda$CDM as a solution when the extra scalar mode is not excited, but different cosmological evolutions driven by the new term are possible. In particular, we show that for a soft Diff breaking, the new contribution always behaves as a cosmological constant at late times. When the extra contribution is not negligible, generically its evolution either behaves as dark energy or tracks the dominant background component. Depending on the initial conditions, solutions in which the universe evolves from an expanding to a contracting phase, eventually recollapsing are also possible.

##### 9.Initial data sets with dominant energy condition admitting no smooth dec spacetime extension

**Authors:**Jonathan Glöckle

**Abstract:** There are two versions of the dominant energy condition (=dec): The original one for Lorentzian manifolds and an associated one for initial data sets. If a Lorentzian manifold satisfies dec, then so does the induced initial set on any embedded spacelike hypersurface. In this article, we discuss the question of a potential converse of this: Is every dec initial data set the induced one on a spacelike hypersurface within a suitably chosen dec Lorentzian manifold? We provide an example showing that in general the answer is no if we require all structures to be smooth.

##### 10.Non-metricity with bounday terms: $f(Q,C)$ gravity and cosmology

**Authors:**Tee-How Loo, Avik De, Emmanuel N. Saridakis

**Abstract:** We formulate $f(Q,C)$ gravity and cosmology. Such a construction is based on the symmetric teleparallel geometry, but apart form the non-metricity scalar $Q$ we incorporate in the Lagrangian the boundary term $C$ of its difference from the standard Levi-Civita Ricci scalar $\mathring R$. We extract the general metric and affine connection field equations, we apply them in a cosmological framework, and making two gauge choices we obtain the modified Friedmann equations. As we show, we acquire an effective dark-energy sector of geometrical origin, which can lead to interesting cosmological phenomenology. Additionally, we may obtain an effective interaction between matter and dark energy. Finally, examining a specific model, we show that we can obtain the usual thermal history of the universe, with the sequence of matter and dark-energy epochs, while the effective dark-energy equation-of-state parameter can be quintessence-like, phantom-like, or cross the phantom-divide during evolution.

##### 1.Rotating detectors in dS/AdS

**Authors:**Hari. K, Dawood Kothawala

**Abstract:** We analyse several aspects of detectors on uniformly accelerated, rotating trajectories in de Sitter ($\Lambda>0$) and anti-de Sitter ($\Lambda<0$) spacetimes, focusing particularly on the periodicity, in (Euclidean) proper time $\tau_{\rm traj}$, of geodesic interval $\tau_{\rm geod}$ between two events on the trajectory. We show that for $\Lambda<0$, $\tau_{\rm geod}$ is periodic in ${\rm i} \tau_{\rm traj}$ for specific values of torsion and acceleration. The periodicity disappears in the limit $\Lambda \to 0$, yielding the well known Minkowski result. The results for stationary rotational trajectories in arbitrary curved spacetime are expressed as a perturbative expansion in curvature. Relevance of the work for Unruh-de Witt detectors in curved spacetimes is highlighted.

##### 2.Cosmological First-Order Vacuum Phase Transitions in an Expanding Anisotropic Universe

**Authors:**A. Savaş Arapoğlu, A. Emrah Yükselci

**Abstract:** We examine the anisotropy originated from a first-order vacuum phase transitions through three-dimensional numerical simulations. We apply Bianchi Type-I metric to our model that has one scalar field minimally coupled to the gravity. We calculate the time evolution of the energy density for the shear scalar and the directional Hubble parameters as well as the power spectra for the scalar field and the gravitational radiation although there are a number of caveats for the tensor perturbations in Bianchi Type-I universe. We run simulations with different mass scales of the scalar field, therefore, in addition to investigation of anisotropy via the shear scalar, we also determine at which mass scale the phase transition completes successfully, hence, neglecting the expansion of the Universe does not significantly affect the results. Finally, we showed that such an event may contribute to the total anisotropy depending on the mass scale of the scalar field and the initial population of nucleated bubbles.

##### 3.Single-rotating Five-dimensional Near-horizon Extremal Geometry in General Relativity

**Authors:**Kamal Hajian

**Abstract:** The geometries with SL$(2,\mathbb{R})$ and some axial U$(1)$ isometries are called ``near-horizon extremal geometries" and are found usually, but not necessarily, in the near-horizon limit of the extremal black holes. We present a new member of this family of solutions in five-dimensional Einstein-Hilbert gravity that has only one non-zero angular momentum. In contrast with the single-rotating Myers-Perry extremal black hole and its near-horizon geometry in five dimensions, this solution has a non-vanishing and finite entropy. Although there is a uniqueness theorem that prohibits the existence of such single-rotating near-horizon geometries in five-dimensional general relativity, this solution has a curvature singularity at one of the poles, which breaks the smoothness conditions in the theorem.

##### 4.Efficient Reduced Order Quadrature Construction Algorithms for Fast Gravitational Wave Inference

**Authors:**Gonzalo Morras, Jose Francisco Nuno Siles, Juan Garcia-Bellido

**Abstract:** Reduced Order Quadrature (ROQ) methods can greatly reduce the computational cost of Gravitational Wave (GW) likelihood evaluations, and therefore greatly speed up parameter estimation analyses, which is a vital part to maximize the science output of advanced GW detectors. In this paper, we do an in-depth study of ROQ techniques applied to GW data analysis and present novel algorithms to enhance different aspects of the ROQ bases construction. We improve upon previous ROQ construction algorithms allowing for more efficient bases in regions of parameter space that were previously challenging. In particular, we use singular value decomposition (SVD) methods to characterize the waveform space and choose a reduced order basis close to optimal and also propose improved methods for empirical interpolation node selection, greatly reducing the error added by the empirical interpolation model. To demonstrate the effectiveness of our algorithms, we construct multiple ROQ bases ranging in duration from 4s to 256s for compact binary coalescence (CBC) waveforms including precession and higher order modes. We validate these bases by performing likelihood error tests and P-P tests and explore the speed up they induce both theoretically and empirically with positive results. Furthermore, we conduct end-to-end parameter estimation analyses on several confirmed GW events, showing the validity of our approach in real GW data.

##### 5.Perturbative quasinormal mode frequencies

**Authors:**Yasuyuki Hatsuda, Masashi Kimura

**Abstract:** We often encounter a situation that black hole solutions can be regarded as continuous deformations of simpler ones, or modify general relativity by continuous parameters. We develop a general framework to compute high-order perturbative corrections to quasinormal mode frequencies in such deformed problems. Our method has many applications, and allows to compute numerical values of the high-order corrections very accurately. For several examples, we perform this computation explicitly, and discuss analytic properties of the quasinormal mode frequencies for deformation parameters.

##### 6.Can wormholes and black holes be distinguished by magnification?

**Authors:**Ke Gao, Lei-Hua Liu

**Abstract:** The magnification effect of wormholes and black holes has been extensively researched. It is crucial to provide a finite distance analysis to understand this magnification phenomenon better. In this article, the rotational Simpson-Visser metric (RSV) is chosen as the focus of research. By calculating the deflection of light in RSV metric, we determine the resulting magnification effect, then applied the RSV metric to specific examples such as the Ellis-Bronnikov wormhole, Schwarzschild black hole, and Kerr black hole (or wormhole) to analyze the magnification. We find that Ellis-Bronnikov wormhole only has single magnification peaks, while Kerr black hole has one to three magnification peaks. In addition, the article's findings suggest that the lensing effect of the Central Black Hole of the Milky Way Galaxy exhibits magnification of multiple peaks. However, it should be noted that these effects are not observable from Earth.

##### 7.Detection of astrophysical gravitational wave sources by TianQin and LISA

**Authors:**Alejandro Torres-Orjuela, Shun-Jia Huang, Zheng-Cheng Liang, Shuai Liu, Hai-Tian Wang, Chang-Qing Ye, Yi-Ming Hu, Jianwei Mei

**Abstract:** TianQin and LISA are space-based laser interferometer gravitational wave (GW) detectors planned to be launched in the mid-2030s. Both detectors will detect low-frequency GWs around $10^{-2}\,{\rm Hz}$, however, TianQin is more sensitive to frequencies above this common sweet-spot while LISA is more sensitive to frequencies below $10^{-2}\,{\rm Hz}$. Therefore, TianQin and LISA will be able to detect the same sources but with different accuracy for different sources and their parameters. We study the detection distance and the detection accuracy with which TianQin and LISA will be able to detect some of the most important astrophysical sources -- massive black hole binaries, stellar-mass black holes binaries, double white dwarfs, extreme mass ratio inspirals, light and heavy intermediate mass ratio inspirals, as well as the stochastic gravitational background produced by binaries. We, further, study the detection distance and detection accuracy from joint detection. We compare the results obtained by the three detection scenarios highlighting the gains from joint detection as well as the contribution of TianQin and LISA to a combined study of astrophysical sources. In particular, we consider the different orientations, lifetimes, and duty cycles of the two detectors to explore how they can give a more complete picture when working together.

##### 8.Comparison of neural network architectures for feature extraction from binary black hole merger waveforms

**Authors:**Osvaldo Gramaxo Freitas, Juan Calderón Bustillo, José A. Font, Solange Nunes, Antonio Onofre, Alejandro Torres-Forné

**Abstract:** We evaluate several neural-network architectures, both convolutional and recurrent, for gravitational-wave time-series feature extraction by performing point parameter estimation on noisy waveforms from binary-black-hole mergers. We build datasets of 100,000 elements for each of four different waveform models (or approximants) in order to test how approximant choice affects feature extraction. Our choices include \texttt{SEOBNRv4P} and \texttt{IMRPhenomPv3}, which contain only the dominant quadrupole emission mode, alongside \texttt{IMRPhenomPv3HM} and \texttt{NRHybSur3dq8}, which also account for high-order modes. Each dataset element is injected into detector noise corresponding to the third observing run of the LIGO-Virgo-KAGRA (LVK) collaboration. We identify the Temporal Convolutional Network (TCN) architecture as the overall best performer in terms of training and validation losses and absence of overfitting to data. Comparison of results between datasets shows that the choice of waveform approximant for the creation of a dataset conditions the feature extraction ability of a trained network. Hence, care should be taken when building a dataset for the training of neural networks, as certain approximants may result in better network convergence of evaluation metrics. However, this performance does not necessarily translate to data which is more faithful to numerical relativity simulations. We also apply this network on actual signals from LVK runs, finding that its feature-extracting performance can be effective on real data.

##### 9.The images of a rotating naked singularity with a complete photon sphere

**Authors:**Mingzhi Wang, Guanghai Guo, Pengfei Yan, Songbai Chen, Jiliang Jing

**Abstract:** For a black hole, the appearance of a shadow is due to the light rays entering the event horizon, and the unstable photon sphere determines the boundary of shadow. Our research indicates that even in the presence of a complete photon sphere without an event horizon, a shadow will not be formed. We present the images of Konoplya-Zhidenko compact object with or without complete photon sphere, and investigate the influence of unstable photon circular orbits (UPCOs) and stable photon circular orbits (SPCOs) on the images of Konoplya-Zhidenko compact object. When the event horizon is absent, the unstable prograde and retrograde light rings can also exist, so dose the complete photon sphere. But the dark shadow doesn't emerge, and the image of the complete photon sphere appears as an infinite number of relativistic Einstein rings. For this case, the light rays pass through the photon sphere, but eventually escape to infinity. For some parameter values, only the unstable retrograde light ring can exist, which leads to an incomplete photon sphere. In this case, the dark shadow also doesn't emerge, and the image of the incomplete photon sphere appears as an infinite number of relativistic Einstein arcs. Furthermore, in Konoplya-Zhidenko naked singularity spacetime, the stable LRs and SPCOs can also exist, but they have no effect on the naked singularity image. This study may contribute to future astronomical observations, and aid in verifying the cosmic censorship conjecture and various gravitational theories.

##### 10.Extreme Light Bending in Spherically-Symmetric Black Hole Spacetimes: Universal Characteristics and Strong-Field Tests of Gravity

**Authors:**Prashant Kocherlakota, Luciano Rezzolla, Rittick Roy, Maciek Wielgus

**Abstract:** Recent images from the Event Horizon Telescope of accreting supermassive black holes (BHs), along with upcoming observations with better sensitivity and angular resolution, offer exciting opportunities to deepen our understanding of spacetime in strong gravitational fields. A significant focus for future BH imaging observations is the direct detection of the "photon ring," a narrow band on the observer's sky that collects extremely lensed photons. The photon ring consists of self-similarly nested subrings which, in spherically-symmetric spacetimes, are neatly indexed by the maximum number of half-loops executed around the BH by the photons that arrive in them. Each subring represents an entire "higher-order" image of the horizon-scale accretion flow. Furthermore, this self-similarity is controlled by a single critical lensing exponent linked to the radial (in)stability of photon orbits near the critical (circular) photon orbit, solely determined by the spacetime geometry. However, extracting such information about the spacetime geometry can be challenging because the observed photon ring is also influenced by the structure of the emitting region. To address this, we conducted a comprehensive study by varying (a) a wide range of emission-zone morphology models and (b) families of spacetime metrics. We find that the lensing exponent can be reliably determined from future observations. This exponent can provide access to the $rr-$component of the spacetime metric, as well as significantly narrow down currently accessible BH parameter spaces. Additionally, the width of the first-order photon subring serves as yet another important discriminator of the spacetime geometry. Finally, observations of flaring events across different wavelengths might reveal time-delayed secondary images, with the delay time providing a promising new way to independently estimate the BH shadow size.

##### 1.Three-dimensional energy-dependent $C$-metric: black hole solutions

**Authors:**B. Eslam Panah

**Abstract:** Considering a three-dimensional $C$-metric and adding energy-dependent to this spacetime, we first create a three-dimensional energy-dependent $C$-metric. Then, we extract accelerating BTZ black hole solutions in gravity's rainbow. Besides, we show that (A)dS black holes cover by an event horizon that depends on all the parameters of this theory. Using the definition of Hawking temperature, we obtain the temperature of these black holes and study the effects of various parameters on this quantity. We find a critical radius in which the temperature is always positive (negative) before (after) it. Then, we obtain the entropy of such black holes. Our analysis indicates that there is the same behavior for entropy, similar to the temperature. Indeed, before (after) the critical radius, the entropy is positive (negative). In order to study the local stability of such black holes, we calculate the heat capacity. We find two different behaviors for the heat capacity, which depend on the cosmological energy-dependent constant. As a final result, accelerating AdS BTZ black holes can satisfy the physical condition and local stability at the same time.

##### 2.The effect of the gravitational constant variation on the propagation of gravitational waves

**Authors:**Jiachen An, Yadong Xue, Zhoujian Cao, Xiaokai He, Bing Sun

**Abstract:** Since the first detection of gravitational waves, they have been used to investigate various fundamental problems, including the variation of physical constants. Regarding the gravitational constant, previous works focused on the effect of the gravitational constant variation on the gravitational wave generation. In this paper, we investigate the effect of the gravitational constant variation on the gravitational wave propagation. The Maxwell-like equation that describes the propagation of gravitational waves is extended in this paper to account for situations where the gravitational constant varies. Based on this equation, we find that the amplitude of gravitational waves will be corrected. Consequently the estimated distance to the gravitational wave source without considering such a correction may be biased. Applying our correction result to the well known binary neutron star coalescence event GW170817, we get a constraint on the variation of the gravitational constant. Relating our result to the Yukawa deviation of gravity, we for the first time get the constraint of the Yukawa parameters in 10Mpc scale. This scale corresponds to a graviton mass $m_g\sim10^{-31}$eV.

##### 3.Gauss-Bonnet solution with a cloud of strings in de Sitter and anti-de Sitter space

**Authors:**Wenxi Zhai, Xiangdong Zhang

**Abstract:** In this paper, we present exact spherically symmetric Gauss-Bonnet black hole solutions surrounded by a cloud of strings fluid with cosmological constant in $D>4$ dimensions. Both charged and uncharged cases are considered. We focus on the de Sitter solutions in the main text and leave the Anti-de Sitter solutions in the appendix. We analyze the features of thermodynamic properties of the black hole solutions. The mass, Hawking temperature as well as thermal stability and the phase transitions are discussed. Moreover, the equation of state and critical phenomena associated with these solutions are also explored.

##### 4.Influence of tachyonic instability on the Schwinger effect in Higgs inflation model

**Authors:**Mehran Kamarpour

**Abstract:** We investigate the influence of the tachyonic instability on the Schwinger effect in Higgs inflation model.In this work we identify the standard horizon scale $ k_{H}=aH $ and the tachyonic instability $ k_{H}=aH|\zeta| , \zeta=\frac{{I}^{\prime}\left(\phi\right)\dot{\phi}}{H} $.This is the horizon scale in which the given Fourier begins to become tachyonically unstable.Influence of this scale appears by vanishing electromagnetic field energy density and energy density of created charged particles due to the Schwinger effect at the very beginning of inflation but does not alter conclusions of our previous work in Refs.\cite{Kamarpour:2022,Kamarpour:2023-I}.We use two coupling functions to break conformal invariance of maxwell action.The simplest coupling function $ I\left(\phi\right)=\chi_{1}\frac{\phi}{M_{p}} $ and a curvature based coupling function $ I\left(\phi\right)= 12\chi_{1}e^{\left(\sqrt{\frac{2}{3}}\frac{\phi}{M_{p}}\right)}\left[\frac{1}{3M_{p}^{2}}\left(4V\left(\phi\right)\right)+\frac{\sqrt{2}}{\sqrt{3}M_{p}}\left(\frac{dV}{d\phi}\right)\right] $ where $V\left(\phi\right) $ is the potential of Higgs inflation in Refs.\cite{Kamarpour:2022,Kamarpour:2023-I}.In fact, we find that only at the very beginning of inflation both energy densities of electromagnetic field and created charged particles vanish due to effect of tachyoinc instability.

##### 1.Two instabilities of Schwarzschild-AdS black holes in Einstein-Weyl-scalar theory

**Authors:**Yun Soo Myung

**Abstract:** Stability of Schwarzschild-AdS (SAdS) black hole is investigated in Einstein-Weyl-scalar (EWS) theory with a negative cosmological constant. Here, we introduce a quadratic scalar coupling to the Weyl term, instead of the Gauss-Bonnet term. The linearized EWS theory admits the Lichnerowicz equation for Einstein tensor as well as scalar equation. The linearized Einstein-tensor carries with a regular mass term (${\cal M}^2$), whereas the linearized scalar has a tachyonic mass term ($-3r_0^2/m^2r^6$). Two instabilities of SAdS black hole in EWS theory are found as Gregory-Laflamme and tachyonic instabilities. It shows that the correlated stability conjecture holds for small SAdS black holes obtained from EWS theory by establishing a close relation between Gregory-Laflamme and thermodynamic instabilities. On the other hand, tachyonic instability of SAdS black hole can be used for making five branches of scalarized black holes when considering proper thermodynamic quantities of EWS theory (${\cal M}^2>0$).

##### 2.Constraints on the Parameters of Modified Chaplygin-Jacobi and Modified Chaplygin-Abel Gases in $f(T)$ Gravity Model

**Authors:**Himanshu Chaudhary, Ujjal Debnath, Tanusree Roy, Sayani Maity, G. Mustafa

**Abstract:** In this study, we investigate two dark energy models, MCJG and MCAG, in the context of $f(T)$ gravity within a non-flat FLRW Universe. Our analysis considers radiation, dark matter, and dark energy components. We compare the equation of state for MCJG and MCAG with $f(T)$ gravity. Using recent astronomical data (e.g., $H(z)$, type Ia supernovae, Gamma Ray Bursts, quasars, and BAO), we constrain the models' parameters and explore the Universe's behavior. The reduced Hubble parameter is expressed in terms of observable parameters like $\Omega_{r0}$, $\Omega_{m0}$, $\Omega_{k0}$, $\Omega_{CJ0}$, $\Omega_{CA0}$, and $H_0$. We investigate cosmic evolution using deceleration, $\mathrm{Om}$, and statefinder diagnostics. Information criteria are employed to assess model viability, comparing against the standard $\Lambda$CDM model. Our objective is to deepen our understanding of dark energy, its relation to $f(T)$ gravity, and the mechanisms governing the accelerated expansion of the Universe.

##### 3.Distinctive Features of Hairy Black Holes in Teleparallel Gauss-Bonnet Gravity

**Authors:**Sebastian Bahamonde, Daniela D. Doneva, Ludovic Ducobu, Christian Pfeifer, Stoytcho S. Yazadjiev

**Abstract:** We examine the teleparallel formulation of non-minimally coupled scalar Einstein-Gauss-Bonnet gravity. In the teleparallel formulation, gravity is described by torsion instead of curvature, causing the usual Gauss-Bonnet invariant expressed through curvature to decay into two separate invariants built from torsion. Consequently, the teleparallel formulation permits broader possibilities for non-minimal couplings between spacetime geometry and the scalar field. In our teleparallel theory, there are two different branches of equations in spherical symmetry depending on how one solves the antisymmetric part of the field equations, leading to a real and a complex tetrad. We first show that the real tetrad seems to be incompatible with the regularity of the equations at the event horizon, which is a symptom that scalarized black hole solutions beyond the Riemannian Einstein-Gauss-Bonnet theory might not exist. Therefore, we concentrate our study on the complex tetrad. This leads to the emergence of scalarized black hole solutions, where the torsion acts as the scalar field source. Extending our previous work, we study monomial non-minimal couplings of degree one and two, which are intensively studied in conventional, curvature-based, scalar Einstein-Gauss-Bonnet gravity. We discover that the inclusion of torsion can potentially alter the stability of the resulting scalarized black holes. Specifically, our findings indicate that for a quadratic coupling, which is entirely unstable in the pure curvature formulation, the solutions induced by torsion may exhibit stability within certain regions of the parameter space. In a limiting case, we were also able to find black holes with a strong scalar field close to the horizon but with a vanishing scalar charge.

##### 4.Notes on no black hole theorem in three dimensional gravity

**Authors:**Pujian Mao, Weicheng Zhao

**Abstract:** In this paper, we revisit the no black hole theorem in three dimensional (3D) gravity in the Newman-Penrose formalism in a generalized Newman-Unti gauge. After adapting the well established 4D NP formalism and its gauge and coordinates system to 3D gravity, we show that the no black hole theorem is manifest in the NP equations. We further study in detail the horizon properties of the 3D charged rotating Martinez-Teitelboim-Zanelli solutions and confirm that a black hole solution requires a negative cosmological constant.

##### 5.TDiff in the Dark: Gravity with a scalar field invariant under transverse diffeomorphisms

**Authors:**Darío Jaramillo-Garrido, Antonio L. Maroto, Prado Martín-Moruno

**Abstract:** We reflect on the possibility of having a matter action that is invariant only under transverse diffeomorphisms. This possibility is particularly interesting for the dark sector, where no restrictions arise based on the weak equivalence principle. In order to implement this idea we consider a scalar field which couples to gravity minimally but via arbitrary functions of the metric determinant. We show that the energy-momentum tensor of the scalar field takes the perfect fluid form when its velocity vector is time-like. We analyze the conservation of this tensor in detail, obtaining a seminal novel result for the energy density of this field in the kinetic dominated regime. Indeed, in this regime the fluid is always adiabatic and we obtain an explicit expression for the speed of sound. Furthermore, to get insight in the gravitational properties of these theories, we consider the fulfillment of the energy conditions, concluding that nontrivial physically reasonable matter violates the strong energy condition in the potential domination regime. On the other hand, we present some shift-symmetric models of particular interest. These are: constant equation of state models (which may provide us with a successful description of dark matter or dark radiation) and models presenting different gravitational domains (characterized by the focusing or possible defocusing of time-like geodesics), as it happens in unified dark matter-energy models.

##### 6.Compact Stars with Dark Energy in General Relativity and Modified Gravity

**Authors:**Artyom V. Astashenok, Sergey D. Odintsov, Vasilis K. Oikonomou

**Abstract:** We investigate realistic models of compact objects, focusing on neutron and strange stars, composed by dense matter and dark energy in the form of a simple fluid or scalar field interacting with matter. For the dark energy component, we use equations of state compatible with cosmological observations. This requirement strongly constrains possible deviations from the simple $\Lambda$-Cold Dark-Matter model with EoS $p_{d}=-\rho_{d}$ at least for small densities of the dark component. But we can propose that the density of dark energy interacting with matter can reach large values in relativistic stars and affects the star parameters such as the mass and radius. Simple models of dark energy are considered. Then we investigated possible effects from modified gravity choosing to study the $R^2$ model combined with dark energy. Finally, the case of dark energy as scalar field non-minimally interacting with gravity is considered.

##### 7.Luminosity of accretion disks around rotating regular black holes

**Authors:**Kuantay Boshkayev, Talgar Konysbayev, Yergali Kurmanov, Orlando Luongo, Marco Muccino, Aliya Taukenova, Ainur Urazalina

**Abstract:** We consider thin accretion disks in the field of a class of rotating regular black holes. For this purpose, we obtain the radius of the innermost stable circular orbit, $r_{ISCO}$ and efficiency of accretion disk in converting matter into radiation $\eta$ with the aim of modeling the disk's emission spectrum. We consider a simple model for the disk's radiative flux, differential and spectral luminosity and compare the results with those expected from accretion disks around Kerr black holes. As a remarkable result, from our computations we find that both the luminosity of the accretion disk and the efficiency are larger in the geometry of rotating regular black holes for fixed and small values of the spin parameter $j$ with respect to those predicted with the Kerr metric for a black hole of the same mass. These results may have interesting implications for astrophysical black holes.

##### 1.Rotating traversable wormhole geometries in the presence of three-form fields

**Authors:**Takol Tangphati
Walailak U., Butsayapat Chaihao
Chula U., Daris Samart
Khon Kaen U., Phongpichit Channuie
Walailak U., Davood Momeni
Northern Virginia Community College

**Abstract:** In this work, we study the rotating wormhole geometries supported by a three-form field. We demonstrate for particular choices of parameters that it is possible for the matter fields threading the wormhole to satisfy the null and weak energy conditions throughout the spacetime, when the three-form field is present. In this case, the form field is interpreted as supporting the wormhole and all the exoticity is confined to it. Thus, the three-form curvature terms, which may be interpreted as a gravitational fluid, sustain these wormhole geometries. Additionally, we also address the ergoregion of the solutions.

##### 2.Scalar Hairy Black Holes with Inverted Mexican Hat Potential

**Authors:**Xiao Yan Chew, Kok-Geng Lim

**Abstract:** We numerically construct the asymptotically flat solutions of hairy black holes supported by a symmetric inverted Mexican hat potential with a local minimum and two degenerate global maxima of a real scalar field that contains a quartic self-interaction term. The solutions of hairy black holes emerge from the Schwarzschild black hole when the non-trivial scalar field exists outside the event horizon. Therefore, we perform a comprehensive study on the properties of the hairy black holes such as the area of horizon, the Hawking temperature, the innermost stable circular orbit, the photon sphere, etc. We also numerically study their linear stability in the mode analysis, hence finding that they are unstable against the linear perturbation.

##### 3.Topology of light rings for extremal and non-extremal Kerr-Newman Taub-NUT black holes without $\mathbb{Z}_2$ symmetry

**Authors:**Shan-Ping Wu, Shao-Wen Wei

**Abstract:** Understanding the light ring, one kind fundamental orbit, shall provide us with novel insight into the astronomical phenomena, such as the ringdown of binary merger and shadow of black holes. Recently, topological approach has preliminarily demonstrated its potential advantages on the properties of the light rings. However, for the black holes without $\mathbb{Z}_2$ symmetry and extremal spinning black holes are remained to be tested. In this paper, we aim at these two issues. Due to the NUT charge, the Kerr-Newman Taub-NUT solution has no $\mathbb{Z}_2$ symmetry. By constructing the corresponding topology for the non-extremal spinning black holes, we find the topological number keeps unchanged. This indicates that $\mathbb{Z}_2$ symmetry has no influence on the topological number, while it indeed affects the locations of the light rings and deviates them off the equatorial plane. For the extremal spinning black holes, we find its topology is critically dependent of the leading term of the vector's radial component at the zero point of its angular component on the black hole horizon. The findings state that there exists a topological phase transition, where the topological number changes, for the prograde light rings. While no phase transition occurs for the retrograde light rings. Our study uncovers some universal topological properties for the extremal and non-extremal spinning black holes with or without $\mathbb{Z}_2$ symmetry. It also has enlightening significance on understanding the light rings in a more general black hole background.

##### 4.Mass Ratio of Binary Black Holes Determined from LIGO/Virgo Data Restricted to Small False Alarm Rate

**Authors:**Tomoya Kinugawa, Takashi Nakamura, Hiroyuki Nakano

**Abstract:** Binary black-hole mergers up to the third observing run with the minimum false alarm rate smaller than $10^{-5}\,{\rm yr}^{-1}$ tell us that the mass ratio of two black holes follows $m_2/m_1=0.723$ with the chance probability of 0.00301% for $M_{chirp} > 18 M_{\odot}$ where $M_{chirp}$ ($= (m_1m_2)^{3/5}/(m_1+m_2)^{1/5}$) is called the chirp mass of binary with masses $m_1$ and $m_2$ ($ < m_1$). We show that the relation of $m_2/m_1=0.723$ is consistent if the binaries consist of population III stars which are the first stars in the universe. On the other hand, it is found for $M_{chirp} < 18 M_{\odot}$ that the mass ratio follows $m_2/m_1=0.601$ with the chance probability of 0.117% if we ignore GW190412 with $m_2/m_1\sim 0.32$. This suggests the different origin from that for $M_{chirp }> 18 M_{\odot}$.

##### 5.Study of scattered light in the main arms of the Einstein Telescope gravitational wave detector

**Authors:**M. Andrés-Carcasona, A. Macquet, M. Martínez, Ll. M. Mir, H. Yamamoto

**Abstract:** We present an estimation of the noise induced by scattered light inside the main arms of the Einstein Telescope (ET) gravitational wave detector. Both ET configurations for high- and low-frequency interferometers are considered, for which we propose baffle layouts. The level of scattered light and the ET laser beam clipping losses are intimately related to the baffle inner aperture. We discuss how this translates into minimum requirements on the vacuum pipe radius, a critical parameter in the ET design. The noise estimations are computed using analytical calculations complemented with numerical tools, and depend on a number of baseline parameters we use as input in the calculations. We conclude that the scattered light noise can be maintained at acceptable levels such that does not compromise the ET performance, provided some requirements are met.

##### 6.Spontaneous Deformation of an AdS Spherical Black Hole

**Authors:**Zhuan Ning, Qian Chen, Yu Tian, Xiaoning Wu, Hongbao Zhang

**Abstract:** In this study, we investigate the real-time dynamics during the spontaneous deformation of an unstable spherical black hole in asymptotically anti-de Sitter (AdS) spacetime. For the initial value, the static solutions with spherical symmetry are obtained numerically, revealing the presence of a spinodal region in the phase diagram. From the linear stability analysis, we find that only the central part of such a thermodynamically unstable spinodal region leads to the emergence of a type of axial instability. To trigger the dynamical instability, an axial perturbation is imposed on the scalar field. As a result, by the fully nonlinear dynamical simulation, the spherical symmetry of the gravitational system is broken spontaneously, leading to the formation of an axisymmetric black hole.

##### 7.Image of a black hole illuminated by a parabolic screen

**Authors:**Elena V. Mikheeva, Sergey V. Repin, Vladimir N. Lukash

**Abstract:** An analytical model of a parabolic screen illuminating a black hole is constructed. This makes it possible to naturally avoid the occurrence of edge effects associated with photons moving along the plane of the screen. The temperature distribution along the radius of the screen corresponds to that for a relativistic disk (Novikov-Thorne disk). It is shown that the structure of the emerging black hole shadow differs significantly from the case when the photon source is a remote screen, since in the model considered, the photons subjected to strong gravitational lensing of the black hole are emitted by the "back side" of the screen, which would not be visible in the absence of a black hole. In the thin screen approximation, the shadow of a Schwarzschild black hole has been constructed in cases when the angle between the axis of symmetry of the illuminating screen and the direction towards the observer is 5, 30, 60, and 80 degrees. For the Kerr black hole, images are shown for angles of 60 and 80 degrees.

##### 1.The role of the boundary term in $f(Q,B)$ symmetric teleparallel gravity

**Authors:**Salvatore Capozziello, Vittorio De Falco, Carmen Ferrara

**Abstract:** In the framework of metric-affine gravity, we consider the role of the boundary term in Symmetric Teleparallel Gravity assuming $f(Q,B)$ models where $f$ is a smooth function of the non-metricity scalar $Q$ and the related boundary term $B$. Starting from a variational approach, we derive the field equations and compare them with respect to those of $f(Q)$ gravity in the limit of $B\to0$. It is possible to show that $f(Q,B)=f(Q-B)$ models are dynamically equivalent to $f(R)$ gravity as in the case of teleparallel $f(\tilde{B}-T)$ gravity (where $B\neq \tilde{B}$). Furtherrmore, conservation laws are derived. In this perspective, considering boundary terms in $ f(Q)$ gravity represents the last ingredient towards the Extended Geometric Trinity of Gravity where $f(R)$, $f(T,\tilde{B})$ and $f(Q,B)$ can be dealt under the same standard.

##### 2.Spacetime-symmetry breaking effects in gravitational-wave generation at the first post-Newtonian order

**Authors:**Nils A. Nilsson, Christophe Le-Poncin Lafitte

**Abstract:** Current searches for signals of departures from the fundamental symmetries of General Relativity using gravitational waves are largely dominated by propagation effects like dispersion and birefringence from highly dynamic sources such as coalescing binary-black holes and neutron stars. In this paper we take steps towards probing the nature of spacetime symmetries in the generation stage of gravitational waves; by using a generic effective-field theory, we solve the modified Einstein equations order-by-order for a generic source, and we write down the the first Post-Newtonian corrections, which includes contributions from the spacetime-symmetry breaking terms. Choosing as the source a system of point particles allows us to write down a simple toy solution explicitly, and we see that in contrast to General Relativity, the monopolar and dipolar contributions are non-vanishing. We comment on the detectability of such signals by the Laser Interferometer Space Antenna (LISA) space mission, which has high signal-to-noise galactic binaries (which can be modelled as point particles) well inside its predicted sensitivity band, sources which are inaccessible for current ground-based detectors, and we also discuss the possibility of going beyond the quadrupole formula and the first Post-Newtonian order, which would reveal effects which could be probed by ground-based detectors observing coalescence events.

##### 3.Classical radiation fields for scalar, electromagnetic, and gravitational waves with spacetime-symmetry breaking

**Authors:**Quentin G. Bailey, Alexander S. Gard, Nils A. Nilsson, Rui Xu, Lijing Shao

**Abstract:** An effective field theory framework is used to investigate some Lorentz-violating effects on the generation of electromagnetic and gravitational waves, complementing previous work on propagation. Specifically we find solutions to a modified, anisotropic wave equation, sourced by charged or fluid matter. We derive the radiation fields for scalars, classical electromagnetic radiation, and partial results for gravitational radiation. For gravitational waves, the results show longitudinal and trace polarizations proportional to coefficients for spacetime-symmetry breaking.

##### 4.Rapid localization and inference on compact binary coalescences with the Advanced LIGO-Virgo-KAGRA gravitational-wave detector network

**Authors:**Soichiro Morisaki, Rory Smith, Leo Tsukada, Surabhi Sachdev, Simon Stevenson, Colm Talbot, Aaron Zimmerman

**Abstract:** We present a rapid parameter estimation framework for compact binary coalescence (CBC) signals observed by the LIGO-Virgo-KAGRA (LVK) detector network. The goal of our framework is to enable optimal source localization of binary neutron star (BNS) signals in low latency, as well as improve the overall scalability of full CBC parameter estimation analyses. Our framework is based on the reduced order quadrature (ROQ) technique, and resolves its shortcomings by utilizing multiple ROQ bases in a single parameter estimation run. We have also developed sets of compact ROQ bases for various waveform models, IMRPhenomD, IMRPhenomPv2, IMRPhenomPv2$\_$NRTidalv2, and IMRPhenomXPHM. We benchmark our framework with hundreds of simulated observations of BNS signals by the LIGO-Virgo detector network, and demonstrate that it provides accurate and unbiased estimates on BNS source location, with a median analysis time of $6$ minutes. The median searched area is reduced by around 30$\%$ compared to estimates produced by BAYESTAR: from $21.8\,\mathrm{deg^2}$ to $16.6\,\mathrm{deg^2}$. Our framework also enables detailed parameter estimation taking into account gravitational-wave higher multipole moments, the tidal deformation of colliding objects, and detector calibration errors of amplitude and phase with the time scale of hours. Our rapid parameter estimation technique has been implemented in one of the LVK parameter estimation engines, BILBY, and is being employed by the automated parameter estimation analysis of the LVK alert system.

##### 5.After collapse: On how a physical vacuum can change the black hole paradigm

**Authors:**Julio Arrechea, Carlos Barceló, Valentin Boyanov

**Abstract:** Standard General Relativity assumes that, in the absence of classical matter sources, spacetime is empty. This chapter considers and analyses the new behaviours of the gravitational field that appear when one substitutes this emptiness by a reactive vacuum, stemming in particular from the idea of vacuum provided by quantum field theory. We restrict our study to spherically symmetric configurations, and take a simple free quantum scalar field as a proxy to more complicated formulations. Our analysis is split into a study of static and of dynamical configurations. Under the assumption of staticity, we find and describe the different asymptotically flat self-consistent solutions that appear when using a vacuum Renormalised Stress-Energy Tensor (RSET) as an additional source in the Einstein equations. Of particular interest is the discovery that, as opposed to standard general relativity, the new theory naturally contains static ultracompact stellar configurations which could observationally be mistaken for black holes (BHs). Then, in our study of dynamical configurations, we investigate the possibility of these same vacuum effects changing the internal gravitational processes after an initial gravitational collapse in a way which shows a path towards forming the aforementioned ultracompact configurations. This has lead us to analyse several dynamical situations seldom contemplated in the literature. Of special relevance, we find that the inner horizon that all realistic BHs should contain could inflate outwards quickly enough to meet the outer one before any appreciable Hawking evaporation has taken place.

##### 6.Gravitational redshift test of EEP with RA from near Earth to the distance of the Moon

**Authors:**N. V. Nunes, N. Bartel, A. Belonenko, G. D. Manucharyan, S. M. Popov, V. N. Rudenko, L. I. Gurvits, G. Cimò, G. Molera Calvés, M. V. Zakhvatkin, M. F. Bietenholz

**Abstract:** The Einstein Equivalence Principle (EEP) is a cornerstone of general relativity and predicts the existence of gravitational redshift. We report on new results of measuring this shift with RadioAstron (RA), a space VLBI spacecraft launched into an evolving high eccentricity orbit around Earth with geocentric distances reaching 353,000 km. The spacecraft and ground tracking stations at Pushchino, Russia, and Green Bank, USA, were each equipped with a hydrogen maser frequency standard allowing a possible violation of the predicted gravitational redshift, in the form of a violation parameter $\varepsilon$, to be measured. By alternating between RadioAstron's frequency referencing modes during dedicated sessions between 2015 and 2017, the recorded downlink frequencies can essentially be corrected for the non-relativistic Doppler shift. We report on an analysis using the Doppler-tracking frequency measurements made during these sessions and find $\varepsilon = (2.1 \pm 3.3)\times10^{-4}$. We also discuss prospects for measuring $\varepsilon$ with a significantly smaller uncertainty using instead the time-domain recordings of the spacecraft signals and envision how $10^{-7}$ might be possible for a future space VLBI mission.

##### 7.Scalarized Black Holes: Extending From and Beyond the Schwarzschild Solution

**Authors:**Xi-Jing Wang, Guoyang Fu, Peng Liu, Xiao-Mei Kuang, Bin Wang, Jian-Pin Wu

**Abstract:** We construct novel scalarized black hole (BH) solutions beyond the general relativity (GR) framework. These scalarized BH solutions are extended from the Schwarzschild one and the non-Schwarzschild one in the pure Einstein-Weyl gravity. By studying the BH entropy and free energy, we demonstrate that the scalarized BH extending from the Schwarzschild one exhibits thermodynamically preferred. We obtain these novel solutions by directly solving the full fourth-order equations of motion. This narrows the problematic solution space obtained by commonly adopted second-order reduction to physically valid spaces. Our findings also unveil the evasion of the no-hair theorem within the realm of higher-derivative gravity.

##### 8.Living on the Edge: Quantum Black Hole Physics from the Event Horizon

**Authors:**Manuel Del Piano, Stefan Hohenegger, Francesco Sannino

**Abstract:** Quantum gravity theories predict deformations of black hole solutions relative to their classical counterparts. A model-independent approach was advocated in \cite{Binetti:2022xdi} that uses metric deformations parametrised in terms of physical quantities, such as the proper distance. While such a description manifestly preserves the invariance of the space-time under coordinate transformations, concrete computations are hard to tackle since the distance is defined in terms of the deformed metric itself. In this work, for spherically symmetric and static metrics, we provide a self-consistent framework allowing us to compute the distance function in close vicinity to the event horizon of a black hole. By assuming a minimal degree of regularity at the horizon, we provide explicit (series) expansions of the metric. This allows us to compute important thermodynamical quantities of the black hole, such as the Hawking temperature and entropy, for which we provide model-independent expressions, beyond a large mass expansion. Moreover, imposing for example the absence of curvature singularities at the event horizon leads to non-trivial consistency conditions for the metric deformations themselves, which we find to be violated by some models in the literature.

##### 9.Interior spacetimes sourced by stationary differentially rotating irrotational cylindrical fluids. III. Azimuthal pressure

**Authors:**M. -N. Célérier

**Abstract:** In a recent series of papers, new exact analytical solutions to field equations of General Relativity representing interior spacetimes sourced by stationary rigidly rotating cylinders of fluids with various equations of state have been displayed. This work is currently extended to the case of differentially rotating irrotational fluids. The results are presented in a new series of papers considering, in turn, a perfect fluid source, arXiv:2305.11565 [gr-qc], as well as the three anisotropic pressure cases already studied in the rigidly rotating configuration. The axially directed pressure case has already been developed in arXiv:2307.07263. Here, a fluid with an azimuthally directed pressure is considered. A general method for generating the corresponding new mathematical solutions to the field equations when the ratio $h=$pressure/energy density varies with the radial coordinate is proposed, and a class of solutions exemplifying this recipe is derived. Then, the case where $h=const.$ is solved. It splits into two subclasses depending on the value of $h$. The mathematical and physical properties of these three classes are analyzed which provides some constraints on $h$, different for each class and subclass. Their matching to an exterior Lewis-Weyl vacuum and the conditions for avoiding an angular deficit are discussed. A comparison with the rigidly rotating fluid case is provided.

##### 10.Modelling the black holes surrounded by a dark matter halo in the galactic center of M87

**Authors:**Dong Liu, Yi Yang, Zhaoyi Xu, Zheng-Wen Long

**Abstract:** In this paper, the structure of a dark matter halo can be well described by the mass model of M87 and the Einasto profile for the cold dark matter model, i.e., $\rho_{\text{halo}} (r)=\rho_e \exp ( -2 \alpha ^{-1} ((r/r_e)^\alpha -1 ) )$ [J. Wang et al., Nature, 585, 39-42 (2020)]. Under these conditions, we construct a solution of a static spherically symmetric black hole in a dark matter halo. Then, using the Newman-janis algorithm, we extend this static solution to the case of rotation, and obtain a solution for the Kerr-like black hole. We prove that this solution of the Kerr-like black hole is indeed a solution to the Einstein field equations. Finally, taking M87 as an example, we study and analyze some physical properties of this Kerr-like black hole, and then compare them with the Kerr black hole. These research results for the black hole in a dark matter halo may indirectly provide an effective method for detecting the existence of dark matter.

##### 11.A class of rotating metrics in the presence of a scalar field

**Authors:**Behrouz Mirza, Parichehr Kangazian Kangazi, Fatemeh Sadeghi

**Abstract:** We consider a class of three parameter static and axially symmetric metrics that reduce to the Janis-Newman-Winicour (JNW) and $ \gamma$-metrics in certain limits of the parameters. We obtain rotating form of the metrics that are asymptotically flat, stationary and axisymmetric. In certain values of the parameters, the solutions represent the rotating JNW metric, rotating $ \gamma$-metric and Bogush-Gal'tsov (BG) metric. The singularities of rotating metrics are investigated. Using the light-ring method, we obtain the quasi normal modes (QNMs) related to rotating metrics in the eikonal limit. Finally, we investigate the precession frequency of a test gyroscope in the presence of the rotating metrics.

##### 12.Real-space quantum-to-classical transition of time dependent background fluctuations

**Authors:**S. Mahesh Chandran
IIT Bombay, Karthik Rajeev
IIT Bombay, S. Shankaranarayanan
IIT Bombay

**Abstract:** Understanding the emergence of classical behavior from a quantum theory is vital to establishing the quantum origin for the temperature fluctuations observed in the Cosmic Microwave Background (CMB). We show that a real-space approach can comprehensively address the quantum-to-classical transition problem in the leading order of curvature perturbations. To this end, we test spatial bipartitions of quadratic systems for the interplay between three different signatures of classical behavior : i) decoherence, ii) peaking of the Wigner function about classical trajectories, and iii) relative suppression of non-commutativity in observables. We extract these signatures from the covariance matrix of a multi-mode Gaussian state and address them primarily in terms of entanglement entropy and log-classicality. Through a phase-space stability analysis of spatial sub-regions via their reduced Wigner function, we ascertain that the underlying cause for the dominance of classicality signatures is the occurrence of gapped inverted mode instabilities. While the choice of conjugate variables enhances some of these signatures, decoherence studied via entanglement entropy is the stronger and more reliable condition for classicality to emerge. We demonstrate the absence of decoherence, which preempts a quantum-to-classical transition of scalar fluctuations in an expanding background in $(1+1)$-dimensions using two examples : i) a Tanh-like expansion and ii) a de-Sitter expansion. We then extend the analysis to leading order fluctuations in $(3+1)-$dimensions to show that a quantum-to-classical transition occurs in the de-Sitter expansion and discuss the relevance of our analysis in distinguishing cosmological models.

##### 13.Ideal gases and degenerate Fermi gases in external torsion fields

**Authors:**Chih-Hung Wang, Yu-Huei Wu

**Abstract:** We investigate the effects of external torsion fields on ideal gases and Fermi gases, and derive a macroscopic quantity, which we call torsion susceptibility. We first consider the Dirac fermions in the Riemann-Cartan spacetime minimally coupled to the background torsion and electromagnetic fields. After applying the Foldy-Wouthuysen transformation, Hamiltonian of a spin-1/2 particle in weak field limit is obtained. The coupling of spin and spatial components of axial torsion vector has a Zeeman-like effect, which removes the degeneracy of energy levels and splits the energy levels with respect to the spin. We calculate the macroscopic effects of the spin-torsion coupling on ideal gases, which satisfying the Boltzmann distribution, and Fermi gases, which satisfying the Fermi-Dirac distribution. The torsion susceptibility of ideal gases is inversely proportional to the temperature and is constant in Fermi gases.

##### 1.Coordinates are messy -- not only in General Relativity

**Authors:**Carla Cederbaum, Melanie Graf

**Abstract:** The coordinate freedom of General Relativity makes it challenging to find mathematically rigorous and physically sound definitions for physical quantities such as the center of mass of an isolated gravitating system. We will argue that a similar phenomenon occurs in Newtonian Gravity once one ahistorically drops the restriction that one should only work in Cartesian coordinates when studying Newtonian Gravity. This will also shed light on the nature of the challenge of defining the center of mass in General Relativity. Relatedly, we will give explicit examples of asymptotically Euclidean relativistic initial data sets which do not satisfy the Regge--Teitelboim parity conditions often used to achieve a satisfactory definition of center of mass. These originate in our joint work with Jan Metzger. This will require appealing to Bartnik's asymptotic harmonic coordinates.

##### 2.Fast and Fourier: Extreme Mass Ratio Inspiral Waveforms in the Frequency Domain

**Authors:**Lorenzo Speri, Michael L. Katz, Alvin J. K. Chua, Scott A. Hughes, Niels Warburton, Jonathan E. Thompson, Christian E. A. Chapman-Bird, Jonathan R. Gair

**Abstract:** Extreme Mass Ratio Inspirals (EMRIs) are one of the key sources for future space-based gravitational wave interferometers. Measurements of EMRI gravitational waves are expected to determine the characteristics of their sources with sub-percent precision. However, their waveform generation is challenging due to the long duration of the signal and the high harmonic content. Here, we present the first ready-to-use Schwarzschild eccentric EMRI waveform implementation in the frequency domain for use with either graphics processing units (GPUs) or central processing units (CPUs). We present the overall waveform implementation and test the accuracy and performance of the frequency domain waveforms against the time domain implementation. On GPUs, the frequency domain waveform takes in median $0.044$ seconds to generate and is twice as fast to compute as its time domain counterpart when considering massive black hole masses $\geq 2 \times 10^6 \,{\rm M_\odot}$ and initial eccentricities $e_0 > 0.2$. On CPUs, the median waveform evaluation time is $5$ seconds, and it is five times faster in the frequency domain than in the time domain. Using a sparser frequency array can further speed up the waveform generation, reaching up to $ 0.3$ seconds. This enables us to perform, for the first time, EMRI parameter inference with fully relativistic waveforms on CPUs. Future EMRI models which encompass wider source characteristics (particularly black hole spin and generic orbit geometries) will require significantly more harmonics. Frequency-domain models will be essential analysis tools for these astrophysically realistic and important signals.

##### 3.Spin-orbit contribution to radiative losses for spinning binaries with aligned spins

**Authors:**Donato Bini, Andrea Geralico, Piero Rettegno

**Abstract:** We compute the leading order contribution to radiative losses in the case of spinning binaries with aligned spins due to their spin-orbit interaction. The orbital average along hyperboliclike orbits is taken through an appropriate spin-orbit modification to the quasi-Keplerian parametrization for nonspinning bodies, which maintains the same functional form, but with spin-dependent orbital elements. We perform consistency checks with existing PN-based and PM-based results. In the former case, we compare our expressions for both radiated energy and angular momentum with those obtained in [JHEP \textbf{04}, 154 (2022)] by applying the boundary-to-bound correspondence to known results for ellipticlike orbits, finding agreement. The linear momentum loss is instead newly computed here. In the latter case, we also find agreement with the low-velocity limit of recent calculations of the total radiated energy, angular momentum and linear momentum in the framework of an extension of the worldline quantum field theory approach to the classical scattering of spinning bodies at the leading post-Minkowskian order [Phys. Rev. Lett. \textbf{128}, no.1, 011101 (2022), Phys. Rev. D \textbf{106}, no.4, 044013 (2022)]. We get exact expressions of the radiative losses in terms of the orbital elements, even if they are at the leading post-Newtonian order, so that their expansion for large values of the eccentricity parameter (or equivalently of the impact parameter) provides higher-order terms in the corresponding post-Minkowskian expansion, which can be useful for future crosschecks of other approaches.

##### 4.A Tribute to S. Deser: Conserved Quantities in Generic Gravity Theories

**Authors:**Bayram Tekin

**Abstract:** I describe parts of my joint work with S. Deser [March 19, 1931 - April 21, 2023] which started when I was working as a post-doc at Brandeis University in 2001. Our work was mostly, but not exclusively, on conserved charges of higher curvature theories of gravity. I also describe some recent developments, such as expressing the conserved charges in terms of the Riemann tensor, but do not add any novel material which has not been published before, however, I expound upon the computations. I also reminisce about our interaction for over two decades that went beyond our scientific collaboration. The physics part of this review is intended for graduate students and researchers interested in extended theories of gravity, especially about the conserved quantities and perturbative techniques in these theories.

##### 5.Absorption cross section in gravity's rainbow from confluent Heun equation

**Authors:**Kihong Kwon, Julián Barragán Amado, Bogeun Gwak

**Abstract:** We investigate the scattering of a massless scalar field by a charged non-rotating black hole in the presence of gravity's rainbow. Using the connection coefficients of the confluent Heun equation expressed in terms of the semi-classical confluent conformal blocks and the instanton part of the Nekrasov-Shatashvili (NS) free energy, we obtain an asymptotic expansion for the low-energy absorption cross section.

##### 6.Bianchi-I cosmologies, magnetic fields and singularities

**Authors:**Roberto Casadio, Alexander Kamenshchik, Panagiotis Mavrogiannis, Polina Petriakova

**Abstract:** We study the effects of a spatially homogenous magnetic field in Bianchi-I cosmological models. In particular, we consider the case of a pure magnetic field and two models with dust and a massless scalar field (stiff matter), respectively. In all these cases, we analyze the approach to the singularity in some detail and comment on the issue of the singularity crossing.

##### 7.Thermodynamic topology and photon spheres in the Hyperscaling violation black hole

**Authors:**Jafar Sadeghi, Mohammad Ali S. Afshar, Saeed Noori Gashti, Mohammad Reza Alipour

**Abstract:** It was shown that a standard ring of light can be imagined outside the event horizon for stationary rotating four-dimensional black holes with axial symmetry using the topological method. Based on this concept, in this paper, we investigate the topological charge and the conditions of existence of the photon sphere (PS) for a hyperscaling violation (HSV) black hole with various values of the parameters of this model. Then, after carrying out a detailed analysis, we show the conventional topological classes viz $Q=-1$ for the mentioned black hole and $Q=0$ for the naked singularities. Also, we propose a new topological class for naked singularities ($Q=+1$) with respect to $z>1$. Then, we will use two different methods, namely the temperature (Duan's topological current $\Phi$-mapping theory) and the generalized Helmholtz free energy method, to study the topological classes of our black hole. By considering the black hole mentioned, we discuss the critical and zero points (topological charges and topological numbers) for different parameters of hyperscaling violating black holes, such as ($z, \theta$) and other free parameters, and study their thermodynamic topology. We observe that for a given value of the parameters $z$, $\theta$, and other free parameters, there exist two total topological charges $(Q_{t}=-1, 0)$ for the $T$ method and two total topological numbers $(W=+1)$ for the generalized Helmholtz free energy method. Additionally, we summarize the results for each study as photon sphere, temperature, and generalized Helmholtz free energy in some figures and tables. Finally, we compare our findings with other related studies in the literature.

##### 8.Higher-dimensional extension of a vacuum-defect wormhole

**Authors:**F. R. Klinkhamer

**Abstract:** We present a 5D metric which interpolates between the standard 4D Schwarzschild metric with mass parameter $M$ and a new 4D $M$-deformed vacuum-defect-wormhole metric. The 5D spacetime can, in principle, have an infinite mass density that gives rise to the $M$ parameter of the 4D $M$-deformed vacuum-defect wormhole.

##### 9.Constraints on the ghost-free parity-violating gravity from Laser-ranged Satellites

**Authors:**Jin Qiao, Zhao Li, Ran Ji, Tao Zhu, Guoliang Li, Wen Zhao

**Abstract:** This paper explores the evolutionary behavior of the Earth-satellite binary system within the framework of the ghost-free parity-violating gravity and the corresponding discussion on the parity-violating effect from the laser-ranged satellites. For this purpose, we start our study with the Parameterized Post-Newtonian (PPN) metric of this gravity theory to study the orbital evolution of the satellites in which the spatial-time sector of the spacetime is modified due to the parity violation. With this modified PPN metric, we calculate the effects of the parity-violating sector of metrics on the time evolution of the orbital elements for an Earth-satellite binary system. We find that among the five orbital elements, the parity violation has no effect on the semi-latus rectum, inclination and ascending node, which are the same as the results of general relativity and consistent with the observations of the current experiment. In particular, parity violation produces non-zero corrections to the eccentricity and pericenter, which will accumulate with the evolution of time, indicating that the parity violation of gravity produces observable effects. The observational constraint on the parity-violating effect is derived by confronting the theoretical prediction with the observation by the LAGEOS II pericenter advance, giving a constraint on the parity-violating parameter space from the satellite experiments.

##### 10.Gravitational Waves Background (NANOGrav) from Quintessential Inflation

**Authors:**Barnali Das, Nur Jaman, M Sami

**Abstract:** We investigate the production process of induced gravity waves due to large scalar fluctuations in the paradigm of quintessential inflation. We numerically solve the Mukhanov-Sasaki equation for different sets of parameters to obtain the power spectra. We demonstrate that the induced gravity wave signal generated in this framework can falls within the region of the NANOGrav data for chosen values of model parameters. We show that there is an allowed region of parameter space where the effect shifts to high frequency regime relevant to LISA and other available sensitivities.

##### 11.Generalized Teleparallel de Sitter geometries

**Authors:**Alan A. Coley, Alexandre Landry, Robert J. van den Hoogen, David D. McNutt

**Abstract:** Theories of gravity based on teleparallel geometries are characterized by the torsion, which is a function of the coframe, derivatives of the coframe, and a zero curvature and metric compatible spin connection. The appropriate notion of a symmetry in a teleparallel geometry is that of an affine symmetry. Due to the importance of the de Sitter geometry and Einstein spaces within general relativity, we shall describe teleparallel de Sitter geometries and discuss their possible generalizations. In particular, we shall analyse a class of Einstein teleparallel geometries which have a 4-dimensional Lie algebra of affine symmetries, and display two one-parameter families of explicit exact solutions.

##### 1.Detecting Extra Dimension By the Experiment of the Quantum Gravity Induced Entanglement of Masses

**Authors:**Shuai Feng, Bao-Min Gu, Fu-Wen Shu

**Abstract:** It is believed that gravity may be regarded as a quantum coherent mediator. In this work we propose a plan using the Quantum Gravity Induced Entanglement of Masses (QGEM) experiment to test the extra dimension. The experiment involves two freely falling test masses passing though a Stern-Gerlach-like device. We study the entanglement witness of them in the framework of Randall-Sundrum II model (RS-II). It turns out that the system would reach entangled more rapidly in the presence of extra dimension. In particular, this is more significant for large radius of extra dimension.

##### 2.Inflation Based on the Tsallis Entropy

**Authors:**Zeinab Teimoori, Kazem Rezazadeh

**Abstract:** We study the inflationary scenario in the Tsallis entropy-based cosmology. The Friedmann equations in this setup can be derived by using the first law of thermodynamics. To derive the relations of the power spectra of the scalar and tensor perturbations in this setup, we reconstruct an $f(R)$ gravity model which is thermodynamically equivalent to our model in the slow-roll approximation. In this way, we find the inflationary observables, including the scalar spectral index and the tensor-to-scalar ratio in our scenario. Then, we investigate two different potentials in our scenario, including the quadratic potential and the potential associated with the natural inflation in which the inflaton is an axion or a pseudo-Nambu-Goldstone boson. We examine their observational viability in light of the Planck 2018 CMB data. We show that although the results of these potentials are in tension with the observations in the standard inflationary setting, their consistency with the observations can be significantly improved within the setup of the Tsallis entropy-based inflation. Moreover, we place constraints on the parameters of the considered inflationary models by using the Planck 2018 data.

##### 3.General Relativistic Fall on a Thick-Plate

**Authors:**Mustafa Halilsoy, Vahideh Memari

**Abstract:** As an extension of a thin-shell, we adopt a single parametric plane-symmetric Kasner-type spacetime to represent an exact thick-plate. This naturally extends the domain wall spacetime to a domain thick-wall case. Physical properties of such a plate with symmetry axis $z$ and thickness $0\leq z\leq z_{0}$ are investigated. Geodesic analysis determines the possibility of a Newtonian-like fall, namely with constant negative acceleration as it is near the Earth's surface. This restricts the Kasner-like exponents to a finely-tuned set, which together with the thickness and energy parameter determine the G-force of the plate. In contrast to the inverse square law, the escape velocity of the thick-shell is unbounded. The metric is regular everywhere but expectedly the energy-momentum of the thick-plate remains problematic.

##### 4.The harmonic background paradigm, or why gravity is attractive

**Authors:**Carlos Barceló, Gil Jannes

**Abstract:** In a work by Visser, Bassett and Liberati (VBL) [Nucl. Phys. B (Proc. Suppl.) 88, 267 (2000)] a relation was suggested between a null energy condition and the censorship of superluminal behaviour. Their result was soon challenged by Gao and Wald [Class. Quantum Grav. 17, 4999, (2000)] who argued that this relation is gauge dependent and therefore lacks physical significance. In this paper, we clear up this controversy by showing that both papers are correct but need to be interpreted in distinct paradigms. In this context, we introduce a new paradigm to interpret gravitational phenomena, which we call the Harmonic Background Paradigm. This harmonic background paradigm starts from the idea that there exists a more fundamental background causality provided by a flat spacetime geometry. One of the consequences of this paradigm is that the VBL relation provides an explanation of why gravity is attractive in all standard weak-field situations.

##### 5.Bianchi Type Cosmological Models in $f(T)$ Tele-parallel Gravity

**Authors:**R. J. van den Hoogen, A. A. Coley, D. D. McNutt

**Abstract:** Symmetry assumptions on the geometrical framework have provided successful mechanisms to develop physically meaningful solutions to many problems. In tele-parallel gravity, invariance of the frame and spin-connection under a group of motions defines an affine symmetry group. Here, we assume there exists a three-dimensional group of affine symmetries acting simply transitively on a spatial hypersurface and that this group of symmetry actions defines our affine frame symmetry group. We determine the general form of the co-frame and spin connection for each spatially homogeneous Bianchi type. We then construct the corresponding field equations for $f(T)$ tele-parallel gravity. We show that if the symmetry group is of Bianchi type A ($I$, $II$, $VI_0$, $VII_0$, $VIII$ or $IX$) then there exists a co-frame/spin connection pair that is consistent with the antisymmetric part of the field equations of $f(T)$ tele-parallel gravity. For those geometries having a Bianchi type B symmetry group ($IV$, $V$, $VI_h$, $VII_h$), we find that in general these geometries are inconsistent with the antisymmetric part of the $f(T)$ tele-parallel gravity field equations unless the theory reduces to an analog of General Relativity with a cosmological constant.

##### 6.Rotating Kiselev Black Holes in $f(R,T)$ Gravity

**Authors:**Sushant G. Ghosh, Shafqat Ul Islam, Sunil D. Maharaj

**Abstract:** Exact solutions describing rotating black holes can provide significant opportunities for testing modified theories of gravity, which are motivated by the challenges posed by dark energy and dark matter. Starting with a spherical Kiselev black hole as a seed metric, we construct rotating Kiselev black holes within the $f(R,T)$ gravity framework using the revised Newman-Janis algorithm - the $f(R,T)$ gravity-motivated rotating Kiselev black holes (FRKBH), which encompasses, as exceptional cases, Kerr ($K=0$) and Kerr-Newman ($K=Q^2$) black holes. These solutions give rise to distinct classes of black holes surrounded by fluids while considering specific values of the equation-of-state parameter, $w$, for viable choices for the $f(R,T)$ function. From the parameter space or domain of existence of black holes defined by $a$ and $\gamma$ for FKRBH, we discover that when $a_1<a<a_2$, there is a critical value $\gamma=\gamma_E$ which corresponds to extreme value black holes portrayed by degenerate horizons. When $a<a_1$ ($a>a_2$), we encounter two distinct critical values $\gamma=\gamma_{E1}, \; \gamma_{E2}$ with $\gamma_{E1}>\gamma_{E2}$ (or $\gamma=\gamma_{E3},\; \gamma_{E4}$ with $\gamma_{E3}>\gamma_{E4}$. We delve into the horizon and global structure of FKRBH spacetimes and examine their dependence on parameters $w$ and $\gamma$. This exploration is motivated by the remarkable effects of $f(R,T)$ gravity, which gives rise to diverse and intricate spacetime structures within the domain where black holes exist.

##### 7.Novel tests of gravity using nano-Hertz stochastic gravitational-wave background signals

**Authors:**Enrico Cannizzaro, Gabriele Franciolini, Paolo Pani

**Abstract:** Gravity theories that modify General Relativity in the slow-motion regime can introduce nonperturbative corrections to the stochastic gravitational-wave background~(SGWB) from supermassive black-hole binaries in the nano-Hertz band, while remaining perturbative in the highly-relativistic regime and satisfying current post-Newtonian~(PN) constraints. We present a model-agnostic formalism to map such theories into a modified tilt for the SGWB spectrum, showing that negative PN corrections (in particular -2PN) can alleviate the tension in the recent pulsar-timing-array data if the detected SGWB is interpreted as arising from supermassive binaries. Despite being preliminary, current data have already strong constraining power, for example they set a novel (conservative) upper bound on theories with time-varying Newton's constant at least at the level of $\dot{G}/G \lesssim 10^{-5} \text{yr}^{-1}$ for redshift $z=[0.1\div1]$. We also show that NANOGrav data are best fitted by a broken power-law interpolating between a dominant -2PN or -3PN modification at low frequency, and the standard general-relativity scaling at high frequency. Nonetheless, a modified gravity explanation should be confronted with binary eccentricity, environmental effects, nonastrophysical origins of the signal, and scrutinized against statistical uncertainties. These novel tests of gravity will soon become more stringent when combining all pulsar-timing-array facilities and when collecting more data.

##### 8.A mean curvature flow method for numerical cosmology

**Authors:**Matthew Doniere, David Garfinkle

**Abstract:** We provide a mean curvature flow method for numerical cosmology and test it on cases of inhomogenous inflation. The results show (in a proof of concept way) that the method can handle even large inhomogeneities that result from different regions exiting inflation at different times.

##### 1.Collisional Penrose process of extended test particles near an extremal Kerr black hole

**Authors:**Aofei Sang, Jie Jiang, Ming Zhang

**Abstract:** We investigate the collisional Penrose process of extended test particles near extremal Kerr black holes using the pole-dipole-quadrupole approximation. We analyze the motion of the test particles and examine the dynamics and maximum efficiency of energy extraction in this process. Our results demonstrate that the maximum extracted energy in the collisional Penrose process is influenced by the spin s and quadrupolar parameter CES2 of the test particles. Specifically, we observe that, at a fixed collisional position, the energy extraction efficiency decreases as the spin increases for either the pole-dipole or the pole-dipole-quadrupole approximation case. Furthermore, for a fixed spin, the energy extraction efficiency is higher in the pole-dipole-quadrupole approximation compared to the pole-dipole approximation. These findings provide insight into the role of the internal structures of the test particles in the collisional Penrose process.

##### 2.Bardeen spacetime as a quantum corrected Schwarzschild black hole: Quasinormal modes and Hawking radiation

**Authors:**R. A. Konoplya, D. Ovchinnikov, B. Ahmedov

**Abstract:** The Bardeen black hole holds historical significance as the first model of a regular black hole. Recently, there have been proposed interpretations of the Bardeen spacetime as quantum corrections to the Schwarzschild solution. Our study focuses on investigating the quasinormal modes and Hawking radiation of the Bardeen black hole. We have observed that previous studies on the quasinormal modes for the Bardeen black hole suffer from inaccuracies that cannot be neglected. Therefore, we propose accurate calculations of the quasinormal modes for scalar, electromagnetic, and neutrino fields in the Bardeen spacetime. Additionally, we have computed the grey-body factors and analyzed the emission rates of Hawking radiation. Even when the quantum correction is small and the fundamental mode only slightly differs from its Schwarzschild value, the first several overtones deviate at an increasingly stronger rate. This deviation leads to the appearance of overtones with very small real oscillation frequencies. This outburst of overtones is closely linked to the fact that the quantum-corrected black hole differs from its classical limit primarily near the event horizon. Moreover, the intensity of the Hawking radiation is significantly suppressed (up to three orders of magnitude) by the quantum correction.

##### 3.Constraints on the spherically symmetric parametrized Rezzolla-Zhidenko spacetime through solar system tests, orbit of S2 star about Sgr A$^\star$ and quasiperiodic oscillations

**Authors:**Sanjar Shaymatov, Bobomurat Ahmedov, Mariafelicia De Laurentis, Mubasher Jamil, Qiang Wu, Anzhong Wang, Mustapha Azreg-Aïnou

**Abstract:** In this paper, we find the higher order expansion parameters $\alpha$ and $\lambda$ of spherically symmetric parametrized Rezzolla-Zhidenko (RZ) spacetime by using its functions of the radial coordinate. We discuss constraints on these parameters through classical tests of weak gravitational field effects in Solar System, observations of the S2 star located in the star cluster close to the Sgr A$^{\star}$, and the observed frequencies for the selected microquasars. Based on this spherically symmetric spacetime we perform the analytic calculations for Solar System effects like perihelion shift, light deflection, and gravitational time delay so as to determine constraints on the parameters by using observational data. In this paper, we restrict our attention to the constraints on these two higher order expansion parameters $\alpha$ and $\lambda$ that survive at the horizon or near the horizon of spherically symmetric metrics. The properties of these two small parameters expansion in RZ parametrization are discussed. We further apply the Monte Carlo Markov Chain (MCMC) simulations to analyze and obtain the constraints on the expansion parameters of spherically symmetric parametrized RZ spacetime by using observations of phenomena of the S2 star. Finally, we consider the epicyclic motions and further derive analytic form of the epicyclic frequencies so that we constrain these expansion parameters of parametrized RZ spacetime by applying the data of the selected microquasars well-known as astrophysical quasiperiodic oscillations (QPOs). Our results demonstrate that the higher order expansion parameters can be given in the range $\alpha\, ,\lambda=(-0.09\, , 0.09)$ and of order $\sim 10^{-2}$ as a consequence of three various tests and observations.

##### 4.Quasinormal modes and late time tails of perturbation fields on a Schwarzschild-like black hole with a global monopole in the Einstein-bumblebee theory

**Authors:**Xiaolin Zhang, Mengjie Wang, Jiliang Jing

**Abstract:** In this paper we complete a systematic study on quasinormal modes (QNMs) and late time tails for scalar, Dirac and Maxwell fields on a spherically symmetric Schwarzschild-like black hole with a global monopole in the Einstein-bumblebee theory. To look for QNMs, we solve the equations of motion numerically by employing both the matrix and the WKB methods, and find good agreements for numeric data obtained by these two techniques in the regime when both are valid. The impact of the bumblebee parameter $c$, the monopole parameter $\eta^2$ and the multipole number $\ell$ on the fundamental QNMs is analyzed in detail. Our results are shown in terms of the QNMs measured by $\sqrt{1+c}\,M$, where $M$ is a black hole mass parameter. We observe, by increasing $c$ ($\eta^2$) with fixed first few $\ell$, that the real part of QNMs increases for all spin fields; while the magnitude of the imaginary part decreases for scalar and Dirac fields but increases for Maxwell fields. By increasing the multipole number $\ell$ with fixed other parameters, we disclose that the real part of QNMs for all spin fields increases while the magnitude of the imaginary part decreases for scalar and Dirac fields but increases for Maxwell fields. In the eikonal limit, QNMs for all spin fields coincide with each other and the real part scale linearly with $\ell$. In particular, \textit{only} the real part of the asymptotic QNMs is dependent on the bumblebee and monopole parameters. In addition, it is shown that the late time behavior is determined not only by the multipole number but also by the bumblebee and monopole parameters, and is distinct for bosonic and fermonic fields. Our results indicate, both in the context of QNMs and late time tails, that the bumblebee field and the monopole field play the same role in determining the dynamic evolution of perturbation fields.

##### 5.Gravitational waves effects in a Lorentz-violating scenario

**Authors:**K. M. Amarilo, M. B. Ferreira Filho, A. A. Araújo Filho, J. A. A. S. Reis

**Abstract:** This paper focuses on how the production and polarization of gravitational waves are affected by spontaneous Lorentz symmetry breaking, which is driven by a self-interacting vector field. Specifically, we examine the impact of a smooth quadratic potential and a non-minimal coupling, discussing the constraints and causality features of the linearized Einstein equation. To analyze the polarization states of a plane wave, we consider a fixed vacuum expectation value (VEV) of the vector field. Remarkably, we verify that a space-like background vector field modifies the polarization plane and introduces a longitudinal degree of freedom. In order to investigate the Lorentz violation effect on the quadrupole formula, we use the modified Green function. Finally, we show that the space-like component of the background field leads to a third-order time derivative of the quadrupole moment, and the bounds for the Lorentz-breaking coefficients are estimated as well.

##### 6.Implications of the NANOGrav results for primordial black holes and Hubble tension

**Authors:**M. Bousder, A. Riadsolh, A. El Fatimy, M. El Belkacemi, H. Ez-Zahraouy

**Abstract:** The purpose of this work is to investigate the formation and evaporation of the primordial black holes in the inflationary scenarios. Thermodynamic parameters such as mass, temperature and entropy are expressed in terms of NANOGrav frequency. By numerical calculations we show that the constraint on the mass range $10^{-5}kg-10^{50}kg$ is well confirmed. We discuss the relation between the redshift and the probability for gravitational wave source populations. A new parameter associated with the frequency and Hubble rate is presented, by which for the spectral index $n_{s}\approx 0.996$ and the Hubble constant $H_{0}\approx 67.27km.s^{-1}.Mpc^{-1}$, the effective Hubble constant is calculated to be $H_{eff,0}\approx 73.24km.s^{-1}.Mpc^{-1} $ which is compatible with the observational data. We make a comparison between the Hubble tension and the primordial perturbations and the expression of the mass loss rate, chemical potential and central charge needed to describe the Hawking evaporation will be established.

##### 7.The Borde-Guth-Vilenkin Theorem in extended de Sitter spaces

**Authors:**William H. Kinney
Univ. at Buffalo, SUNY, USA, Suvashis Maity
Indian Insitute of Technology, Madras, India, L. Sriramkumar
Indian Insitute of Technology, Madras, India

**Abstract:** The Borde-Guth-Vilenkin (BGV) theorem states that any spacetime with net positive expansion must be geodesically incomplete. We derive a new version of the theorem using the fluid flow formalism of General Relativity. The theorem is purely kinematic, depending on the local expansion properties of geodesics, and makes no assumptions about energy conditions. We discuss the physical interpretation of this result in terms of coordinate patches on de Sitter space, and apply the theorem to Penrose's model of Conformal Cyclic Cosmology. We argue that the Conformal Cyclic extension of an asymptotically de Sitter universe is geodesically incomplete.

##### 8.Existence of Wormhole Solutions in $f(Q,T)$ Gravity under Non-commutative Geometries

**Authors:**Moreshwar Tayde, Zinnat Hassan, P. K. Sahoo

**Abstract:** In this paper, we have systematically discussed the existence of the spherically symmetric wormhole solutions in the framework of $f(Q,\,T)$ gravity under two interesting non-commutative geometries such as Gaussian and Lorentzian distributions of the string theory. Also, to find the solutions, we consider two $f(Q,\,T)$ models such as linear $f(Q,\,T)=\alpha\,Q+\beta\,T$ and non-linear $f(Q,\,T)=Q+\lambda\,Q^2+\eta\,T$ models in our study. We obtained analytic and numerical solutions for the above models in the presence of both non-commutative distributions. We discussed wormhole solutions analytically for the first model and numerically for the second model and graphically showed their behaviors with the appropriate choice of free parameters. We noticed that the obtained shape function is compatible with the flare-out conditions under asymptotic background. Further, we checked energy conditions at the wormhole throat with throat radius $r_0$ and found that NEC is violated for both models under non-commutative background. At last, we examine the gravitational lensing phenomenon for the precise wormhole model and determine that the deflection angle diverges at the wormhole throat.

##### 9.Cosmological evolution from modified Bekenstein entropy law

**Authors:**Marco de Cesare, Giulia Gubitosi

**Abstract:** We study the dynamics of the homogeneous and isotropic cosmological background in the recently proposed ``quantum phenomenological gravitational dynamics'', characterised by logarithmic corrections to the Bekenstein entropy. We show that the model admits a family of solutions that are self-accelerating both at early and late times: they approach de Sitter in the future and admit a past attractor corresponding to an inflationary acceleration era. On the other hand, there are no solutions corresponding to a primordial bounce. We also show that asking scalar perturbations to be unaffected by instabilities on observable scales puts stringent constraints on the deviations from general relativity encoded by the model.

##### 10.Maxwell-Dirac system in cosmology

**Authors:**Bijan Saha

**Abstract:** Within the scope of a Bianchi type-I (BI) cosmological model we study the interacting system of spinor and electromagnetic fields and its role in the evolution of the Universe. In some earlier studies it was found that in case of a pure spinor field the presence of nontrivial non-diagonal components of EMT leads to some severe restrictions both on the spacetime geometry and/or spinor field itself, whereas in case of electromagnetic field with induced nonlinearity such components impose severe restrictions on metric functions and the components of the vector potential. It is shown that in case of interacting spinor and electromagnetic fields restrictions are not as severe as in other cases and in this case a nonlinear and massive spinor field with different components of vector potential can survive in a general Bianchi type-I spacetime.

##### 11.Local first law of black hole

**Authors:**Pabitra Tripathy, Pritam Nanda, Amit Ghosh

**Abstract:** We investigated the form and implications of the local first law of black hole thermodynamics in relation to an observer located at a finite distance from the black hole horizon. Our study is based on the quasilocal form of the first law for black hole thermodynamics, given by $\delta E=\frac{\bar{\kappa}}{8\pi}\delta A$, where $\delta E$ and $\delta A$ represent the changes in the black hole mass and area, respectively, and $\bar{\kappa}$ denotes the quasilocal surface gravity. We show that even at a finite distance, the quasilocal law still holds. It shows how the first law scales with the observer's location.

##### 12.Global Kruskal-Szekeres coordinates for Reissner-Nordström spacetime

**Authors:**Farshid Soltani

**Abstract:** I derive a smooth and global Kruskal-Szekeres coordinate chart for the maximal extension of the non-extremal Reissner-Nordstr\"om geometry that provides a generalization to the standard inner and outer Kruskal-Szekeres coordinates. The Kruskal-Szekeres diagram associated to this coordinate chart, whose existence is an interesting fact in and on itself, provides a simple alternative with a transparent physical interpretation to the conformal diagram of the spacetime.

##### 13.Uniqueness of maximal spacetime boundaries

**Authors:**Melanie Graf, Marco van den Beld-Serrano

**Abstract:** Given an extendible spacetime one may ask how much, if any, uniqueness can in general be expected of the extension. Locally, this question was considered and comprehensively answered in a recent paper of Sbierski, where he obtains local uniqueness results for anchored spacetime extensions of similar character to earlier work for conformal boundaries by Chru\'sciel. Globally, it is known that non-uniqueness can arise from timelike geodesics behaving pathologically in the sense that there exist points along two distinct timelike geodesics which become arbitrarily close to each other interspersed with points which do not approach each other. We show that this is in some sense the only obstruction to uniqueness of maximal future boundaries: Working with extensions that are manifolds with boundary we prove that, under suitable assumptions on the regularity of the considered extensions and excluding the existence of such ''intertwined timelike geodesics'', extendible spacetimes admit a unique maximal future boundary extension. This is analogous to results of Chru\'sciel for the conformal boundary.

##### 14.Quantum dynamics for massless particles in Brinkmann spacetimes

**Authors:**Álvaro Duenas-Vidal, Jorge Segovia

**Abstract:** In Classical Dynamics, Eisenhart lift connects the dynamics of null geodesics in a Brinkmann spacetime with a continuous family of Hamiltonian systems by means of a suitable projection. In this work we explore the possibility of building a model for quantum dynamics of massless particles propagating inside a Brinkmann spacetime from the Einsenhart lift. As a result, we describe spatial tunneling between regions classically disconnected for certain class of null geodesics because of curvature. Also we describe entangled states arising from observers who have a limited access to the whole Brinkmann space. Finally we explore the possibility to find a quantum field theory behind these quantum phenomena.

##### 1.Quasinormal Modes and Greybody factors of AdS/dS Black holes surrounded by Quintessence in Rastall gravity

**Authors:**Dhruba Jyoti Gogoi, N. Heidari, J. Kříž, H. Hassanabadi

**Abstract:** In this work, we have studied the quasinormal modes and greybody factors of AdS/dS Reissner-Nordstr\"om black hole surrounded by quintessence field in Rastall gravity. The violation of energy-momentum conservation has a non-linear effect on the quasinormal modes. With an increase in the black hole charge, both real part of quasinormal modes i.e. oscillation frequency of ring-down Gravitational Waves (GWs) and damping or decay rate of GWs increase non-linearly. A similar observation is made for the black hole structural parameter also, however in this case the variation is almost linear. In the case of greybody factors also, we observed that both the parameters have similar impacts. With an increase in these parameters, greybody factors decrease. Our study suggests that the presence of a surrounding quintessence field may shadow the existence of black hole charge in such black hole configurations.

##### 2.Stochastic Ricci Flow dynamics of the gravitationally induced wave-function collapse

**Authors:**Matteo Lulli, Antonino Marciano, Kristian Piscicchia

**Abstract:** In order to reconcile the wave-function collapse in quantum mechanics with the finiteness of signals' propagation in general relativity, we delve into a stochastic version of the Ricci flow and study its non-relativistic limit in presence of matter. We hence derive the Di\'osi-Penrose collapse model for the wave-function of a quantum gas. The procedure entails additional parameters with respect to phenomenological models hitherto accounted for, including the temperature of the gas and the cosmological constant, in turn related to the stochastic gravitational noise responsible for the collapse.

##### 3.GWDALI: A Fisher-matrix based software for gravitational wave parameter-estimation beyond Gaussian approximation

**Authors:**Josiel Mendonça Soares de Souza, Riccardo Sturani

**Abstract:** We introduce GWDALI, a new Fisher-matrix, python based software that computes likelihood gradients to forecast parameter-estimation precision of arbitrary network of terrestrial gravitational wave detectors observing compact binary coalescences. The main new feature with respect to analogous software is to assess parameter uncertainties beyond Fisher-matrix approximation, using the derivative approximation for Likelihood (DALI). The software makes optional use of the LSC algorithm library LAL and the stochastic sampling algorithm Bilby, which can be used to perform Monte-Carlo sampling of exact or approximate likelihood functions. As an example we show comparison of estimated precision measurement of selected astrophysical parameters for both the actual likelihood, and for a variety of its derivative approximations, which turn out particularly useful when the Fisher matrix is not invertible.

##### 1.Reduced Kiselev black hole

**Authors:**Zhi-Shuo Qu, Towe Wang, Chao-Jun Feng

**Abstract:** The Kiselev model describes a black hole surrounded by a fluid with equations of state $p_r/\rho=-1$ and $p_t/\rho=(3w+1)/2$ respectively in radial and tangential directions. It has been extensively studied in the parameter region $-1<w<-1/3$. If one rids off the black hole and turns to the region $-1/3<w<0$, i.e. $p_t>0$, then a new horizon of black hole type will emerge. This case has been mentioned in Kiselev's pioneer work but seldom investigated in the literature. Referring to it as reduced Kiselev black hole, we revisit this case with attention to its causal structure, thermodynamics, shadow cast and weak-field limit. An alternative interpretation and extensions of the black hole are also discussed.

##### 2.Bulk-boundary correspondences and unique continuation in asymptotically Anti-de Sitter spacetimes

**Authors:**Arick Shao

**Abstract:** This article surveys the research presented by the author at the MATRIX Institute workshop "Hyperbolic Differential Equations in Geometry and Physics" in April 2022. The work is centered about establishing rigorous mathematical statements toward the AdS/CFT correspondence in theoretical physics, in particular in dynamical settings. The contents are mainly based on the recent paper with G. Holzegel that proved a unique continuation result for the Einstein-vacuum equations from asymptotically Anti-de Sitter (aAdS) conformal boundaries. We also discuss some preceding results, in particular novel Carleman estimates for wave equations on aAdS spacetimes, which laid the foundations toward the main correspondence theorems.

##### 3.Sensitivity of Space-based Gravitational-Wave Interferometers to Ultralight Bosonic Fields and Dark Matter

**Authors:**Jiang-Chuan Yu, Yue-Hui Yao, Yong Tang, Yue-Liang Wu

**Abstract:** Ultralight bosonic fields (ULBFs) are predicted by various theories beyond the standard model of particle physics and are viable candidates of cold dark matter. There have been increasing interests to search for the ULBFs in physical and astronomical experiments. In this paper, we investigate the sensitivity of several planned space-based gravitational-wave interferometers to ultralight scalar and vector fields. Using time-delay interferometry (TDI) to suppress the overwhelming laser frequency noise, we derive the averaged transfer functions of different TDI combinations to scalar and vector fields, and estimate the impacts of bosonic field's velocities. We obtain the sensitivity curves for LISA, Taiji and TianQin, and explore their projected constraints on the couplings between ULBFs and standard model particles, illustrating with the ULBFs as dark matter.

##### 4.Gravitational Faraday rotation of light propagation in the Kerr-Newman-Taub-NUT space-time

**Authors:**Hongying Guo

**Abstract:** We investigate the gravitational Faraday effect in the Kerr-Newman-Taub-NUT space-time under the weak deflection limit. Contrary to previously stated zero net effect when the source and the observer are remote from the black hole, a non-zero Faraday rotation has been found. The rotation angle is dependent on the spin and the mass of the black hole and the observer's angular position, as in the case of the Kerr space-time, with additional contribution of the electrical charge and the NUT charge.

##### 5.Neural network time-series classifiers for gravitational-wave searches in single-detector periods

**Authors:**A. Trovato, É. Chassande-Mottin, M. Bejger, R. Flamary, N. Courty

**Abstract:** The search for gravitational-wave signals is limited by non-Gaussian transient noises that mimic astrophysical signals. Temporal coincidence between two or more detectors is used to mitigate contamination by these instrumental glitches. However, when a single detector is in operation, coincidence is impossible, and other strategies have to be used. We explore the possibility of using neural network classifiers and present the results obtained with three types of architectures: convolutional neural network, temporal convolutional network, and inception time. The last two architectures are specifically designed to process time-series data. The classifiers are trained on a month of data from the LIGO Livingston detector during the first observing run (O1) to identify data segments that include the signature of a binary black hole merger. Their performances are assessed and compared. We then apply trained classifiers to the remaining three months of O1 data, focusing specifically on single-detector times. The most promising candidate from our search is 2016-01-04 12:24:17 UTC. Although we are not able to constrain the significance of this event to the level conventionally followed in gravitational-wave searches, we show that the signal is compatible with the merger of two black holes with masses $m_1 = 50.7^{+10.4}_{-8.9}\,M_{\odot}$ and $m_2 = 24.4^{+20.2}_{-9.3}\,M_{\odot}$ at the luminosity distance of $d_L = 564^{+812}_{-338}\,\mathrm{Mpc}$.

##### 6.Three parameter metrics in the presence of a scalar field in four and higher dimensions

**Authors:**Alireza Azizallahi, Behrouz Mirza, Arash Hajibarat, Homayon Anjomshoa

**Abstract:** We investigate a class of three parameter metrics that contain both $\gamma$-metric (Zipoy-Voorhees) and Janis-Newman-Winicour (JNW) metric at special values of the parameters. We derive some properties of the class of metrics such as the effective potential, circular orbits and epicyclic frequencies. We also introduce the five and higher dimensional forms of the class of metrics.

##### 7.Rotating black bounces surrounded by the string cloud

**Authors:**Yi Yang, Dong Liu, Ali Övgün, Zheng-Wen Long, Gaetano Lambiase

**Abstract:** Traversable wormholes and regular black holes usually represent completely different scenarios. But in the black bounce spacetime they can be described by a same line element, which is very attractive. Rodrigues et al. introduced a black bounces spacetime surrounded by the string cloud, which demonstrates that the existence of the string cloud makes the black bounces spacetime remain regular. On the other hand, the black hole photos taken by EHT show that black holes have spin, so spin is an indispensable intrinsic property of black holes in the real universe. In this work, we used the Newman-Janis method to introduce spin into black bounces surrounded by the string cloud. We investigate the effect of the spin $a$ and string cloud parameter $L$ on the shadow of black bounces surrounded by the string cloud. We find that shadow in this spacetime is very sensitive to the $L$ , i.e., the string cloud parameter can significantly increase the boundary of the shadow.

##### 8.Testing the nonclassicality of gravity with the field of a single delocalized mass

**Authors:**Alessandro Pesci, Pierbiagio Pieri

**Abstract:** Most of the existing proposals for laboratory tests of a quantum nature of gravity are based on the use of two delocalized masses or harmonically bound masses prepared in pure quantum states with large enough spatial extent. Here, a setup is proposed that is based on on a single delocalized mass coupled to a harmonically-trapped test mass (undergoing first expansion and then compression) that moves under the action of gravity. We investigate the in-principle feasibility of such an experiment, which turns out to crucially depend on the ability to tame Casimir forces. We thus proceed with a design aimed at achieving this, trying at the same time to take advantage of these forces rather than only fighting them.

##### 9.Geodesically completing regular black holes by the Simpson-Visser method

**Authors:**Kunal Pal, Kuntal Pal, Tapobrata Sarkar

**Abstract:** Regular black holes are often geodesically incomplete when their extensions to negative values of the radial coordinate are considered. Here, we propose to use the Simpson-Visser method of regularising a singular spacetime, and apply it to a regular solution that is geodesically incomplete, to construct a geodesically complete regular solution. Our method is generic, and can be used to cure geodesic incompleteness in any spherically symmetric static regular solution, so that the resulting solution is symmetric in the radial coordinate. As an example, we illustrate this procedure using a regular black hole solution with an asymptotic Minkowski core. We study the structure of the resulting metric, and show that it can represent a wormhole or a regular black hole with a single or double horizon per side of the throat. Further, we construct a source Lagrangian for which the geodesically complete spacetime is an exact solution of the Einstein equations, and show that this consists of a phantom scalar field and a nonlinear electromagnetic field. Finally, gravitational lensing properties of the geodesically complete spacetime are briefly studied.

##### 10.Explaining Large Electromagnetic Logarithms from Loops of Inflationary Gravitons

**Authors:**D. Glavan
CEICO, S. P. Miao
NCKU, T. Prokopec
Utrecht, R. P. Woodard
Florida

**Abstract:** Recent progress on nonlinear sigma models on de Sitter background has permitted the resummation of large inflationary logarithms by combining a variant of Starobinsky's stochastic formalism with a variant of the renormalization group. We reconsider single graviton loop corrections to the photon wave function, and to the Coulomb potential, in light of these developments. Neither of the two 1-loop results have a stochastic explanation, however, the flow of a curvature-dependent field strength renormalization explains their factors of $\ln(a)$. We speculate that the factor of $\ln(Hr)$ in the Coulomb potential should not be considered as a leading logarithm effect.

##### 1.Second-order cosmological perturbations. V. Produced by scalar-scalar coupling during inflation stage

**Authors:**Bo Wang, Yang Zhang

**Abstract:** We study the perturbations up to the 2nd-order for a power-law inflation driven by a scalar field in synchronous coordinates. We solve the 1st-order perturbed Einstein equation and scalar field equation, give the 1st-order solutions for all the scalar, vector, and tensor metric perturbations, as well as the perturbed scalar field. During inflation, the 1st-order tensor perturbation is a wave and is decoupled from other perturbations, the scalar metric perturbation and the perturbed scalar field are coupled waves, propagating at the speed of light, differing from those in the dust and relativistic fluid models. The 1st-order vector perturbation is not wave and just decreases during inflation. The 2nd-order perturbed Einstein equation is similar in structure to the 1st-order one, but various products of the 1st-order perturbations occur as the effective source, among which the scalar-scalar coupling is considered in this paper. The solutions of all the 2nd-order perturbations consist of a homogeneous part similar to the 1st-order solutions, and an inhomogeneous part in a form of integrations of the effective source. The 2nd-order vector perturbation is also a wave since the effective source is composed of the 1st-order waves. We perform the residual gauge transformations between synchronous coordinates up to the 2nd-order, and identify the 1st-order and 2nd-order gauge modes. The 1st-order tensor perturbation is gauge independent, and all others are gauge dependent. We examine four 1st-order gauge invariant scalar perturbations and use the zero-point energy of the scalar field to determine the four primordial spectra.

##### 2.Probing naked singularities in the charged and uncharged $γ$-metrics with quantum wave packets

**Authors:**Ozay Gurtug, Mustafa Halilsoy, Mert Mangut

**Abstract:** The non-trivial naked singularities that possess directional behavior in the charged and uncharged Zipoy-Voorhees (ZV) spacetimes, known as {\gamma} - metrics are investigated within the context of quantum mechanics. Classically singular spacetime is understood as a geodesic incompleteness with respect to a particle probe, while quantum singularity is understood as a non-unique evolution of test quantum wave packets. In this study, quantum wave packets obeying Klein - Gordon equation are used to probe timelike naked singularities. It is shown by rigorous mathematical calculations that the outermost singularity developed in the charged and uncharged Zipoy-Voorhees spacetime on the equatorial plane is quantum mechanically singular for all values of the deformation parameter {\gamma}. However, directional singularities that develop on the symmetry axis is shown to be healed partially for specific range of the parameter {\gamma}, if the analysis is restricted purposely to only specific mode (s-wave mode). Allowing arbitrary modes, classical directional singularities remains quantum singular.

##### 3.Scattering of Maxwell potentials on curved spacetimes

**Authors:**Grigalius Taujanskas

**Abstract:** We report on the recent construction of a scattering theory for Maxwell potentials on curved spacetimes.

##### 4.EHT observables as a tool to estimate parameters of supermassive black holes

**Authors:**Misba Afrin, Sushant G. Ghosh

**Abstract:** The Event Horizon Telescope (EHT) collaboration unveiled event-horizon-scale images of the supermassive black holes (SMBHs) M87* and Sgr A*, revealing a dark brightness depression, namely the black hole shadow, whose shape and size may encode the parameters of the SMBHs, and the shadow is consistent with that of a Kerr black hole. It furnishes another encouraging tool to estimate black hole parameters and test theories of gravity in extreme regions near the event horizon. We propose a technique that uses EHT observables, the angular shadow diameter $d_{sh}$ and the axis ratio $\mathcal{D}_A$, to estimate the parameters associated with SMBHs, described by the Kerr metric. Unlike previous methods, our approach explicitly considers the uncertainties in the measurement of EHT observables. Modelling Kerr--Newman and three rotating regular spacetimes to be M87* and Sgr A* and applying our technique, we estimate the associated charge parameters along with spin. Our method is consistent with the existing formalisms and can be applied to shadow shapes that are more general and may not be circular. We can use the technique for other SMBHs once their EHT observables become accessible. With future, more accurate measurements of the EHT observables, the estimation of various SMBH parameters like the spin and inclination angles of M87* and Sgr A* would be more precise.

##### 5.Geodesics motion of test particles around Schwarzschild-Klinkhamer wormhole with topological defects and gravitational lensing

**Authors:**Faizuddin Ahmed

**Abstract:** This study investigates the geodesic motion of test particles, both massless and massive, within a Schwarzschild-Klinkhamer (SK) wormhole space-time. We specifically consider the influence of cosmic strings on the system and analyze the effective potential, and observing that the presence of a cosmic string parameter alters it for null and time-like geodesics. Moreover, we calculate the deflection angle for null geodesics, and demonstrate that the cosmic string modifies this angle and induces a shift in the results. Additionally, we extend our investigation in this SK-wormhole space-time but with a global monopole. We explore the geodesic motion of test particles in this scenario and find that the effective potential is affected by the global monopole. Similarly, we determine the deflection angle for null geodesics and show that the global monopole parameter introduces modifications to this angle. Lastly, we present several known solutions for space-times involving cosmic strings and global monopoles within the framework of this SK-wormhole

##### 6.Scalar-induced gravitational wave interpretation of PTA data: the role of scalar fluctuation propagation speed

**Authors:**Shyam Balaji, Guillem Domènech, Gabriele Franciolini

**Abstract:** Pulsar timing arrays gathered evidence of the presence of a gravitational wave background around nHz frequencies. If the gravitational wave background was induced by large and Gaussian primordial fluctuations, they would then produce too many sub-solar mass primordial black holes. We show that if at the time of gravitational wave generation the universe was dominated by a canonical scalar field, with the same equation of state as standard radiation but a higher propagation speed of fluctuations, one can explain the gravitational wave background with a primordial black hole counterpart consistent with observations. Lastly, we discuss possible ways to test this model with future gravitational wave detectors.

##### 7.Towards numerical-relativity informed effective-one-body waveforms for dynamical capture black hole binaries

**Authors:**Tomas Andrade, Juan Trenado, Simone Albanesi, Rossella Gamba, Sebastiano Bernuzzi, Alessandro Nagar, Juan Calderon-Bustillo, Nicolas Sanchis-Gual, Jose A. Font, William Cook, Boris Daszuta, Francesco Zappa, David Radice

**Abstract:** Dynamical captures of black holes may take place in dense stellar media due to the emission of gravitational radiation during a close passage. Detection of such events requires detailed modelling, since their phenomenology qualitatively differs from that of quasi-circular binaries. Very few models can deliver such waveforms, and none includes information from Numerical Relativity (NR) simulations of non quasi-circular coalescences. In this study we present a first step towards a fully NR-informed Effective One Body (EOB) model of dynamical captures. We perform 14 new simulations of single and double encounter mergers, and use this data to inform the merger-ringdown model of the TEOBResumS-Dali approximant. We keep the initial energy approximately fixed to the binary mass, and vary the mass-rescaled, dimensionless angular momentum in the range $(0.6, 1.1)$, the mass ratio in $(1, 2.15)$ and aligned dimensionless spins in $(-0.5, 0.5)$. We find that the model is able to match NR to $97%$, improving previous performances, without the need of modifying the base-line template. Upon NR informing the model, this improves to $99%$ with the exception of one outlier corresponding to a direct plunge. The maximum EOBNR phase difference at merger for the uninformed model is of $0.15$ radians, which is reduced to $0.1$ radians after the NR information is introduced. We outline the steps towards a fully informed EOB model of dynamical captures, and discuss future improvements.

##### 1.Interior spacetimes sourced by stationary differentially rotating irrotational cylindrical fluids. II. Axial pressure

**Authors:**M. -N. Célérier

**Abstract:** In a recent series of papers new exact analytical solutions of Einstein equations representing interior spacetimes sourced by stationary rigidly rotating cylinders of fluids have been displayed. We have first considered a fluid with an axially directed pressure C\'el\'erier, Phys. Rev. D 104, 064040 (2021), J. Math. Phys. 64, 032501 (2023), then a perfect fluid, J. Math. Phys. 64, 022501 (2023), followed by a fluid with an azimuthally directed pressure, J. Math. Phys. 64, 042501 (2023), and finally a fluid where the anisotropic pressure is radially oriented, J. Math. Phys. 64, 052502 (2023). This work is being currently extended to the cases of differentially rotating irrotational fluids. The results are presented in a new series of papers considering, in turn, a perfect fluid source, arXiv:2305.11565 [gr-qc], and the same three anisotropic pressure cases. Here, fluids with an axially directed pressure are considered. A general method for generating new mathematical solutions to the field equations is displayed and three classes are presented so as to exemplify this recipe. Their mathematical and physical properties are analyzed. The first class, named class A, whose other mathematical and physical properties determine a standard configuration, is shown to exhibit a singular axis of symmetry which can be considered as an awkward drawback. The second class, class B, is free from such a singularity but appears to exhibit a negative energy density which characterizes a rather exotic kind of matter. The third class, class C, is the best behaved since it possesses the main properties expected from spacetimes sourced by rather standard fluids. The three classes are matched to an exterior Lewis-Weyl vacuum and the conditions for avoiding an angular deficit are discussed. A comparison with the rigidly rotating fluid case is provided.

##### 2.Infinite derivative gravity resolves nonscalar curvature singularities

**Authors:**Ivan Kolář, Tomáš Málek

**Abstract:** We explicitly demonstrate that the nonlocal ghost-free ultraviolet modification of general relativity (GR) known as the infinite derivative gravity (IDG) resolves nonscalar curvature singularities in exact solutions of the full theory. We analyze exact pp-wave solutions of GR and IDG describing gravitational waves generated by null radiation. Curvature of GR and IDG solutions with the same energy-momentum tensor is compared in parallel-propagated frames along timelike and null geodesics at finite values of the affine parameter. While the GR pp-wave solution contains a physically problematic nonscalar curvature singularity at the location of the source, the curvature of its IDG counterpart is finite.

##### 3.Quasinormal modes of black holes encircled by a gravitating thin disk

**Authors:**Che-Yu Chen, Petr Kotlařík

**Abstract:** The ringdown phase of gravitational waves emitted by a perturbed black hole is described by a superposition of exponentially decaying sinusoidal modes, called quasinormal modes (QNMs), whose frequencies depend only on the property of the black hole geometry. The extraction of QNM frequencies of an isolated black hole would allow for testing how well the black hole is described by general relativity. However, astrophysical black holes are not isolated. It remains unclear whether the extra matter surrounding the black holes such as accretion disks would affect the validity of the black hole spectroscopy when the gravitational effects of the disks are taken into account. In this paper, we study the QNMs of a Schwarzschild black hole superposed with a gravitating thin disk. Considering up to the first order of the mass ratio between the disk and the black hole, we find that the existence of the disk would decrease the oscillating frequency and the decay rate. In addition, within the parameter space where the disk model can be regarded as physical, there seems to be a universal relation that the QNM frequencies tend to obey. The relation, if it holds generically, would assist in disentangling the QNM shifts caused by the disk contributions from those induced by other putative effects beyond general relativity. The QNMs in the eikonal limit, as well as their correspondence with bound photon orbits in this model, are briefly discussed.

##### 4.On the perturbative formalism and a possible quantum discrete spectrum for the Regge-Wheeler equation of a de Sitter spacetime

**Authors:**Stefano Viaggiu

**Abstract:** In this paper we study the perturbative regime in the static patch of de Sitter metric in the Regge-Wheeler formalism. After realizing that perturbative regime in a de Sitter spacetime depicted in terms of usual spherical coordinates cannot be extended up to the cosmological horizon, we study perturbative equations, in particular the axial ones, in terms of the tortoise coordinate $r_*$. We show that perturbative regime can be extended up to the cosmological horizon, provided that suitable boundary conditions are chosen. As an application, we explore the Regge-Wheeler equation at short distances by performing a taylor expansion. In order to study some possible quantum effects at short distances, we impose to the equation so obtained the same boundary conditions suitable for a quantum 3D harmonic oscillator. As a result, a discrete spectrum can be obtained. The aforementioned spectrum is analysed and a relation with possible effects denoting quantum behavior of gravitons is suggested.

##### 5.Regularizing Rotating Black Strings: a new black bounce solution

**Authors:**Arthur Lima, Geová Alencar, Diego Sáez-Chillon Gómez

**Abstract:** The present paper is devoted to a new black bounce solution that regularize the well-known rotating black string in $3+1$ dimensions. To do so, the procedure pointed out by Simpson-Visser is followed, which has been already applied successfully to other static cases of black strings, with and without electric charge. This method implies to force a bounce on the radial coordinate, such that a wormhole throat arises before the singularity, which renders a regular solution. An analysis of the metric is conducted, showing the interpolation between a regular black hole and a wormhole, what provides a much richer family of solutions than the original metric. Different curvature magnitudes are obtained in order to analyze the regularity of the solution, including the Ricci and Kretschmann scalars. Finally, by following the Einstein field equations the corresponding effective energy-momentum tensor is obtained and the energy conditions are analyzed.

##### 6.Quasinormal modes of rotating black holes in higher-derivative gravity

**Authors:**Pablo A. Cano, Kwinten Fransen, Thomas Hertog, Simon Maenaut

**Abstract:** We compute the spectrum of linearized gravitational excitations of black holes with substantial angular momentum in the presence of higher-derivative corrections to general relativity. We do so perturbatively to leading order in the higher-derivative couplings and up to order fourteen in the black hole angular momentum. This allows us to accurately predict quasinormal mode frequencies of black holes with spins up to about $70\%$ of the extremal value. For some higher-derivative corrections, we find that sizable rotation enhances the frequency shifts by almost an order of magnitude relative to the static case.

##### 7.Canonical Quantization of Teukolsky fields on Kerr Background

**Authors:**Claudio Iuliano, Jochen Zahn

**Abstract:** Electromagnetic and gravitational perturbations on Kerr spacetime can be reconstructed from solutions to the Teukolsky equations. We study the canonical quantization of solutions to these equations for any integer spin. Our quantization scheme involves the analysis of the Hertz potential and one of the Newman-Penrose scalars, which must be related via the Teukolsky-Starobinsky identities. We show that the canonical commutation relations between the fields can be implemented if and only if the Teukolsky-Starobinsky constants are positive, which is the case both for gravitational perturbations and Maxwell fields. We also obtain the Hadamard parametrix of the Teukolsky equation, which is the basic ingredient for a local and covariant renormalization scheme for non-linear observables. We also discuss the relation of the canonical energy of Teukolsky fields to that of gravitational perturbations.

##### 1.A well-balanced discontinuous Galerkin method for the first--order Z4 formulation of the Einstein--Euler system

**Authors:**Michael Dumbser, Olindo Zanotti, Elena Gaburro, Ilya Peshkov

**Abstract:** In this paper we develop a new well-balanced discontinuous Galerkin (DG) finite element scheme with subcell finite volume (FV) limiter for the numerical solution of the Einstein--Euler equations of general relativity based on a first order hyperbolic reformulation of the Z4 formalism. The first order Z4 system, which is composed of 59 equations, is analyzed and proven to be strongly hyperbolic for a general metric. The well-balancing is achieved for arbitrary but a priori known equilibria by subtracting a discrete version of the equilibrium solution from the discretized time-dependent PDE system. Special care has also been taken in the design of the numerical viscosity so that the well-balancing property is achieved. As for the treatment of low density matter, e.g. when simulating massive compact objects like neutron stars surrounded by vacuum, we have introduced a new filter in the conversion from the conserved to the primitive variables, preventing superluminal velocities when the density drops below a certain threshold, and being potentially also very useful for the numerical investigation of highly rarefied relativistic astrophysical flows. Thanks to these improvements, all standard tests of numerical relativity are successfully reproduced, reaching three achievements: (i) we are able to obtain stable long term simulations of stationary black holes, including Kerr black holes with extreme spin, which after an initial perturbation return perfectly back to the equilibrium solution up to machine precision; (ii) a (standard) TOV star under perturbation is evolved in pure vacuum ($\rho=p=0$) up to $t=1000$ with no need to introduce any artificial atmosphere around the star; and, (iii) we solve the head on collision of two punctures black holes, that was previously considered un--tractable within the Z4 formalism.

##### 2.Boundary terms and Brown-York quasi-local parameters for scalar-tensor theory: a study on both timelike and null hypersurfaces

**Authors:**Krishnakanta Bhattacharya, Kazuharu Bamba

**Abstract:** Boundary term and Brown-York (BY) formalism, which is based on the Hamilton-Jacobi principle, are complimentary of each other as the gravitational actions are not, usually, well-posed. In scalar-tensor theory, which is an important alternative to GR, it has been shown that this complementarity becomes even more crucial in establishing the equivalence of the BY quasi-local parameters in the two frames which are conformally connected. Furthermore, Brown-York tensor and the corresponding quasi-local parameters are important from two important yet different aspects of gravitational theories: black hole thermodynamics and fluid-gravity correspondence. The investigation suggests that while the two frames are equivalent from the thermodynamic viewpoints, they are not equivalent from the perspective of fluid-gravity analogy or the membrane paradigm. In addition, the null boundary term and null Brown-York formalism are the recent developments (so far obtained only for GR) which is non-trivial owing to the degeneracy of the null surface. In the present analysis these are extended for scalar-tensor theory. The present analysis also suggests that, regarding the equivalence (or inequivalence) of the two frame, the null formalism draws the same inferences as of the timelike case, which in turn establishes the consistency of the newly developed null Brown-York formalism.

##### 3.Photon rings as tests for alternative spherically symmetric geometries with thin accretion disks

**Authors:**Luís F. Dias da Silva, Francisco S. N. Lobo, Gonzalo J. Olmo, Diego Rubiera-Garcia

**Abstract:** The imaging by the Event Horizon Telescope (EHT) of the supermassive central objects at the heart of the M87 and Milky Way (Sgr A$^\star$) galaxies, has marked the first step into peering at the shadow and photon rings that characterize the optical appearance of black holes surrounded by an accretion disk. Recently, Vagnozzi et. al. [S.~Vagnozzi, \textit{et al.} arXiv:2205.07787 [gr-qc]] used the claim by the EHT that the size of the shadow of Sgr A$^\star$ can be inferred by calibrated measurements of the bright ring enclosing it, to constrain a large number of spherically symmetric space-time geometries. In this work we use this result to study some features of the first and second photon rings of a restricted pool of such geometries in thin accretion disk settings. The emission profile of the latter is described by calling upon three analytic samples belonging to the family introduced by Gralla, Lupsasca and Marrone, in order to characterize such photon rings using the Lyapunov exponent of nearly bound orbits and discuss its correlation with the luminosity extinction rate between the first and second photon rings. We finally elaborate on the chances of using such photon rings as observational discriminators of alternative black hole geometries using very long baseline interferometry.

##### 4.The perturbation in Einstein-Gauss-Bonnet gravity \uppercase\expandafter{\romannumeral2}: the quasi-normal modes of the tensor-type of the Kaluza-Klein black hole

**Authors:**Li-Ming Cao, Liang-Bi Wu, Yaqi Zhao, Yu-Sen Zhou

**Abstract:** In Einstein-Gauss-Bonnet gravity, we study the quasi-normal modes (QNMs) of the tensor perturbation for the so-called Maeda-Dadhich black hole which locally has a topology $\mathcal{M}^n \simeq M^4 \times \mathcal{K}^{n-4}$. Our discussion is based on the tensor perturbation equation derived in~\cite{Cao:2021sty}, where the Kodama-Ishibashi gauge invariant formalism for Einstein gravity theory has been generalized to the Einstein-Gauss-Bonnet gravity theory. With the help of characteristic tensors for the constant curvature space $\mathcal{K}^{n-4}$, we investigate the effect of extra dimensions and obtain the scalar equation in four dimensional spacetime, which is quite different from the Klein-Gordon equation. Using the asymptotic iteration method and the numerical integration method with the Kumaresan-Tufts frequency extraction method, we numerically calculate the QNM frequencies. In our setups, characteristic frequencies depend on six distinct factors. They are the spacetime dimension $n$, the Gauss-Bonnet coupling constant $\alpha$, the black hole mass parameter $\mu$, the black hole charge parameter $q$, and two ``quantum numbers" $l$, $\gamma$. Without loss of generality, the impact of each parameter on the characteristic frequencies is investigated while fixing other five parameters. Interestingly, the dimension of compactification part has no significant impact on the lifetime of QNMs.

##### 5.Primordial Power Spectrum in Modified Cosmology: From Thermodynamics of Spacetime to Loop Quantum Cosmology

**Authors:**Ana Alonso-Serrano, Guillermo A. Mena Marugan, Antonio Vicente-Becerril

**Abstract:** We investigate the implications for cosmology of a phenomenological quantum gravity approach based on thermodynamics. We analyze in detail the corresponding primordial power spectrum. The considered modified cosmological scenario has similarities with Loop Quantum Cosmology. Actually, one recovers the same effective background dynamics by fixing the value of the free parameter of the modified approach. In particular, the background experiences a bounce that solves the initial singularity. Adopting background-dependent equations for the primordial perturbations like those derived in General Relativity, the studied model can be considered a generalization of the dressed metric formalism in Loop Quantum Cosmology. We focus our discussion on the spectrum of tensor perturbations. For these perturbations, we compute the exact form of the background-dependent effective mass that affects their propagation. Since there are background regimes in the modified cosmology that are far away from slow-roll inflation, we do not have at our disposal a privileged vacuum like the Bunch-Davies state. We then select the state of the perturbations by a recently proposed criterion that removes unwanted oscillations in the power spectrum. Finally, we numerically compute the spectrum of this vacuum and compare it with other spectra obtained in the literature, especially with one corresponding to an alternative quantization prescription in Loop Quantum Cosmology (called the hybrid prescription).

##### 6.Blandford-Znajek jets in MOdified Gravity

**Authors:**Filippo Camilloni, Troels Harmark, Marta Orselli, Maria J. Rodriguez

**Abstract:** General relativity (GR) will be imminently challenged by upcoming experiments in the strong gravity regime, including those testing the energy extraction mechanisms for black holes. Motivated by this, we explore magnetospheric models and black hole jet emissions in MOdified Gravity (MOG) scenarios. Specifically, we construct new power emitting magnetospheres in a Kerr-MOG background which are found to depend non-trivially on the MOG deformation parameter. This may allow for high-precision tests of GR. In addition, a complete set of analytic solutions for vacuum magnetic field configurations around static MOG black holes are explicitly derived, and found to comprise exclusively Heun polynomials.

##### 7.Suppression of matter density growth at scales exceeding the cosmic screening length

**Authors:**Maxim Eingorn, Ezgi Yilmaz, A. Emrah Yükselci, Alexander Zhuk

**Abstract:** One of the main objectives of modern cosmology is to explain the origin and evolution of cosmic structures at different scales. The principal force responsible for the formation of such structures is gravity. In a general relativistic framework, we have shown that matter density contrasts do not grow over time at scales exceeding the cosmic screening length, which corresponds to a cosmological scale of the order of two to three gigaparsecs at the present time, at which gravitational interactions exhibit an exponential cut-off. This is a purely relativistic effect. To demonstrate the suppression of density growth, we have performed N-body simulations in a box with a comoving size of $5.632\,{\rm Gpc}/h$ and obtained the power spectrum of the mass density contrast. We have shown that it becomes independent of time for scales beyond the cosmic screening length as a clear manifestation of the cosmic screening effect.

##### 1.Early dark energy induced by non-linear electrodynamics

**Authors:**H. B. Benaoum, Luz Ángela García, Leonardo Castañeda

**Abstract:** In this work, we introduce a parametrization of early dark energy that mimics radiation at early times and governs the present acceleration of the Universe. We show that such parametrization models non-linear electrodynamics in the early Universe and investigate the cosmological viability of the model. In our scenario, the early dark energy is encoded in the non-linearity of the electromagnetic fields through a parameter $\beta$ that changes the Lagrangian of the system, and the parameters $\gamma_s$ and $\alpha$, that define the departure from the standard model constant equation of state. We use a Bayesian method and the modular software \textsc{CosmoSIS} to find the best values for the model's free parameters with precomputed likelihoods from Planck 2018, primordial nucleosynthesis data, inferred distances from different wide galaxy surveys and luminosity distances of SNIa from Pantheon and SH0ES, such that $\gamma_s =$ 0.468 $\pm$ 0.026 and $\alpha =$ -0.947 $\pm$ 0.032, as opposed to $\Lambda$CDM where $\gamma_s = \beta =$ 0 and there is no equivalence for the $\alpha$ parameter. Our results predict an earlier formation of the structure and a shorter age of the Universe compared with the canonical cosmological model. One of the main findings of our work is that this kind of dark energy alleviates the ongoing tensions in cosmology, the Hubble tension and the so-called $\sigma_8$ tension, which predicted values by our model are H$_o =$ 70.2 $\pm$ 0.9 km/s/Mpc and $\sigma_8 =$ 0.798 $\pm$ 0.007. The reported values lie between the inferred values inferred from early and late (local) Universe observations. Future observations will shed light on the nature of the dark energy, its impact on the structure formation, and its dynamics.

##### 2.Effective metric of spinless binaries with radiation-reaction effect up to fourth Post-Minkowskian order in effective-one-body theory

**Authors:**Jiliang Jing, Weike Deng, Sheng Long, Jieci Wang

**Abstract:** By means of the scattering angles, we obtain an effective metric of spinless binaries with radiation-reaction effects up to fourth post-Minkowskian order, which is the foundation of the effective-one-body theory. We note that there are freedoms for the parameters of the effective metric because one equation corresponds to two parameters for each post-Minkowskian order. Accordingly, in order to construct a self-consistent effective-one-body theory in which the Hamiltonian, radiation-reaction forces and waveforms for the ``plus" and ``cross" modes of the gravitational wave should be based on the same physical model, we can fix these freedoms by requiring the null tetrad component of the gravitationally perturbed Weyl tensor $\Psi_4^B$ to be decoupled in the effective spacetime.

##### 3.Entanglement from rotating black holes in thermal baths

**Authors:**Ivan Agullo, Anthony J. Brady, Adrià Delhom, Dimitrios Kranas

**Abstract:** We extend previous efforts to quantify the entanglement generated in Hawking's evaporation process by including rotation and thermal environments (e.g. the cosmic microwave background). Both extensions are needed to describe real black holes in our universe. Leveraging techniques from Gaussian quantum information, we find that the black hole's ergoregion is an active source of quantum entanglement and that thermal environments drastically degrade entanglement generation. Our predictions are suitable to be tested in the lab using analogue platforms and also provide tools to assess the fate of quantum information for black holes in more generic settings.

##### 4.A generalized mass-to-horizon relation: a new global approach to entropic cosmologies and its connection to \texorpdfstring{$Λ$}{Lambda}CDM

**Authors:**Hussain Gohar, Vincenzo Salzano

**Abstract:** In this letter, we propose a new generalized mass-to-horizon relation to be used in the context of entropic cosmologies and holographic principle scenarios. We show that a general scaling of the mass with the Universe horizon as $M=\gamma \frac{c^2}{G}L^n$ leads to a new generalized entropy $S_n = \gamma \frac{n}{1+n}\frac{2 \pi\,k_B\,c^3}{G\,\hbar} L^{n+1}$ from which we can recover many of the recently proposed forms of entropies at cosmological and black hole scales and also establish a thermodynamically consistent relation between each of them and Hawking temperature. We analyse the consequences of introducing this new mass-to-horizon relation on cosmological scales by comparing the corresponding modified Friedmann, acceleration, and continuity equations to cosmological data. We find that when $n=3$, the entropic cosmology model is fully and totally equivalent to the standard $\Lambda$CDM model, thus providing a new fundamental support for the origin and the nature of the cosmological constant. In general, if $\log \gamma < -3$, and irrespective of the value of $n$, we find a very good agreement with the data comparable with $\Lambda$CDM from which, in Bayesian terms, our models are indistinguishable.

##### 5.The physical acceptability conditions and the strategies to obtain anisotropic compact objects

**Authors:**Daniel Suárez-Urango, Laura M. Becerra, Justo Ospino, Luis A. Núñez

**Abstract:** We studied five methods to include anisotropy, or unequal stress distributions, in general relativistic matter configurations. We used nine acceptability conditions that the metric and physical variables must meet to determine if our models were astrophysically viable. Our analysis found the most effective way to introduce anisotropy while keeping a simple density profile. We also found a practical "rule of thumb'' that relates the density at the boundary to the density at the centre of relativistic matter distributions. Additionally, we calculated the configuration radius and encountered that values observed by NICER for PSR J0740+6620 are consistent with several acceptable matter configurations, both isotropic and anisotropic.

##### 6.The first law for stationary axisymmetric multi-black hole systems

**Authors:**Gérard Clément, Dmitry Gal'tsov

**Abstract:** In the framework of Einstein-Maxwell theory, we consider collinear arrays of rotating electrically charged black holes connected by Misner-Dirac strings carrying gravimagnetic and magnetic fluxes. The first law of mechanics for these systems is derived. It involves as dynamical variables the areas, angular momenta and electric charges of the various Killing horizons -- black holes and Misner strings. When the gravimagnetic fluxes all vanish, the first law reduces to a form where the dynamical variables associated with the strings are the string tensions and magnetic fluxes. This form is not generically invariant under electric-magnetic duality.

##### 1.Signatures of Ultralight Bosons in Compact Binary Inspiral and Outspiral

**Authors:**Yan Cao, Yong Tang

**Abstract:** Ultralight bosons are well-motivated particles from various physical and cosmological theories, and can be spontaneously produced during the superradiant process, forming a dense hydrogen-like cloud around the spinning black hole. After the growth saturates, the cloud slowly depletes its mass through gravitational-wave emission. In this work we study the orbit dynamics of a binary system containing such a gravitational atom saturated in various spin-0,1,2 superradiant states, taking into account both the effects of dynamical friction and the cloud mass depletion. We estimate the significance of mass depletion, finding that although dynamical friction could dominate the inspiral phase, it typically does not affect the outspiral phase driven by the mass depletion. Focusing on the large orbit radius, we investigate the condition to observe the outspiral, and the detectability of the cloud via pulsar-timing signal in the case of black hole-pulsar binary.

##### 2.Ranging Sensor Fusion in LISA Data Processing: Treatment of Ambiguities, Noise, and On-Board Delays in LISA Ranging Observables

**Authors:**Jan Niklas Reinhardt, Martin Staab, Kohei Yamamoto, Jean-Baptiste Bayle, Aurélien Hees, Olaf Hartwig, Karsten Wiesner, Gerhard Heinzel

**Abstract:** Interspacecraft ranging is crucial for the suppression of laser frequency noise via time-delay interferometry (TDI). So far, the effect of on-board delays and ambiguities in the LISA ranging observables was neglected in LISA modelling and data processing investigations. In reality, on-board delays cause offsets and timestamping delays in the LISA measurements, and PRN ranging is ambiguous, as it only determines the range up to an integer multiple of the pseudo-random noise (PRN) code length. In this article, we identify the four LISA ranging observables: PRN ranging, the sideband beatnotes at the interspacecraft interferometer, TDI ranging, and ground-based observations. We derive their observation equations in the presence of on-board delays, noise, and ambiguities. We then propose a three-stage ranging sensor fusion to combine these observables in order to gain optimal ranging estimates. We propose to calibrate the on-board delays on ground and to compensate the associated offsets and timestamping delays in an initial data treatment (stage 1). We identify the ranging-related routines, which need to run continuously during operation (stage 2), and implement them numerically. Essentially, this involves the reduction of ranging noise, for which we develop a Kalman filter combining the PRN ranging and the sideband beatnotes. We further implement crosschecks for the PRN ranging ambiguities and offsets (stage 3). We show that both ground-based observations and TDI ranging can be used to resolve the PRN ranging ambiguities. Moreover, we apply TDI ranging to estimate the PRN ranging offsets.

##### 3.Conservative binary dynamics from gravitational tail emission processes

**Authors:**Gabriel Luz Almeida, Alan Müller, Stefano Foffa, Riccardo Sturani

**Abstract:** We re-analyze the far zone contribution to the two-body conservative dynamics arising from interaction between radiative and longitudinal modes, the latter sourced by mass and angular momentum, which in the mass case is known as tail process. We verify the expected correspondence between two loop self-energy amplitudes and the gluing of two classical (one leading order, one at one loop) emission amplitudes. In particular we show that the factorization of the self-energy amplitude involving the angular momentum is violated when applying standard computation procedures, due to a violation of the Lorentz gauge condition commonly adopted in perturbative computations. We show however that a straightforward fix exists, as the violation corresponds to a consistent anomaly, and it can be re-absorbed by the variation of a suitable action functional.

##### 4.Phenomenology of DSR-relativistic in-vacuo dispersion in FLRW spacetime

**Authors:**Giovanni Amelino-Camelia, Domenico Frattulillo, Giulia Gubitosi, Giacomo Rosati, Suzana Bedic

**Abstract:** Studies of in-vacuo dispersion are the most active area of quantum-gravity phenomenology. The way in which in-vacuo dispersion produces redshift-dependent corrections to the time of flight of astrophysics particles depends on the model-dependent interplay between Planck-scale effects and spacetime curvature/expansion, and we here derive the most general formula for the leading order redshift-dependent correction to the time of flight for the scenario in which relativistic symmetries are deformed at the Planck scale (DSR). We find that, contrary to the broken symmetries scenario (LIV), where in principle any arbitrary form of redshift dependence could be allowed, for the DSR scenario only linear combinations of three possible forms of redshift dependence are allowed. We also discuss some specific combinations of these three terms whose investigation might deserve priority from the quantum-gravity perspective.

##### 5.Uniform Boundedness for Solutions to the Teukolsky Equation on Schwarzschild from Conservation Laws of Linearised Gravity

**Authors:**Sam C. Collingbourne, Gustav Holzegel

**Abstract:** We consider the equations of linearised gravity on the Schwarzschild spacetime in a double null gauge. Applying suitably commuted versions of the conservation laws derived in earlier work of the second author we establish control on the gauge invariant Teukolsky quantities $\alpha^{[\pm 2]}$ without any reference to the decoupled Teukolsky wave equation satisfied by these quantities. More specifically, we uniformly bound the energy flux of all first derivatives of $\alpha^{[\pm 2]}$ along any outgoing cone from an initial data quantity at the level of first derivatives of the linearised curvature and second derivatives of the linearised connection components. Analogous control on the energy fluxes along any ingoing cone is established a posteriori directly from the Teukolsky equation using the outgoing bounds.

##### 6.Coercivity Properties of the Canonical Energy in Double Null Gauge

**Authors:**Sam C. Collingbourne

**Abstract:** In this paper, we study the canonical energy associated with solutions to the linearised vacuum Einstein equation on a stationary spacetime. The main result of this paper establishes, in the context of the $4$-dimensional Schwarzschild exterior, a direct correspondence between the conservation law satisfied by the canonical energy and the conservation laws deduced by Holzegel for gravitational perturbations in double null gauge. Since the latter exhibit useful coercivity properties (leading to energy and pointwise boundedness statements) we obtain coercivity results for the canonical energy in the double null gauge as a corollary. More generally, the correspondence suggests a systematic way to uncover coercivity properties in the conservation laws for the canonical energy on Kerr.

##### 1.New results on the dynamics of critical collapse

**Authors:**Jun-Qi Guo, Yu Hu, Pan-Pan Wang, Cheng-Gang Shao

**Abstract:** We study the dynamics of critical collapse of a spherically symmetric scalar field. Approximate analytic expressions for the metric functions and matter field in the large-radius region are obtained. It is found that because of the boundary conditions at the center, in the central region, the equation of motion for the scalar field is reduced to the flat-spacetime form. On the other hand, due to the connection to its neighbouring region where gravity plays an important role, the scalar field in the central region feels the gravitational effects indirectly.

##### 2.Challenging event horizons with spin (3/2) fields

**Authors:**Koray Düztaş

**Abstract:** We attempt to destroy the event horizons of Kerr black holes by perturbing them with massless spin (3/2) fields. We carry out a detailed analysis by incorporating the explicit form of the absorption probabilities and backreaction effects due to the self energy of the test fields. For extremal and nearly extremal black holes, backreaction effects dominate for perturbations with large magnitudes. However, small perturbations can destroy the event horizons of extremal black holes and drive nearly extremal black holes closer to extremality. Eventually, nearly extremal black holes reach a certain stage where they can be continuously driven to extremality and beyond. Both the cosmic censorship conjecture and the third law of black hole dynamics can be violated by spin (3/2) fields. This directly follows from the fact that fermionic fields do not satisfy the null energy condition. Therefore this result does not contradict with the fact that cosmic censorship and the laws of black hole mechanics remain valid for perturbations satisfying the null energy condition.

##### 3.Global stability of the open Milne spacetime

**Authors:**Jinhua Wang, Wei Yuan

**Abstract:** The open Milne cosmological spacetime has a 3-dimensional Cauchy surface isometric to the (non-compact) hyperbolic space. We prove the globally nonlinear stability of the open Milne spacetime for both massive and massless Einstein-scalar field equations and show that as time goes to infinity, the spatial metric tends to the hyperbolic metric. The proof is based on the Gaussian normal coordinates, in which the decay rates of gravity are determined by the expanding geometry of Milne spacetime.

##### 4.Constraints on primordial curvature power spectrum with pulsar timing arrays

**Authors:**Zhi-Qiang You, Zhu Yi, You Wu

**Abstract:** The stochastic signal detected by NANOGrav, PPTA, EPTA, and CPTA can be explained by the scalar-induced gravitational waves. In order to determine the scalar-induced gravitational waves model that best fits the stochastic signal, we employ both single- and double-peak parameterizations for the power spectrum of the primordial curvature perturbations, where the single-peak scenarios include the $\delta$-function, box, lognormal, and broken power law model, and the double-peak scenario is described by the double lognormal form. Using Bayesian inference, we find that there is no significant evidence for or against the single-peak scenario over the double-peak model, with $\log$ (Bayes factors) among these models $\ln \mathcal{B} < 1$. Therefore, we are not able to distinguish the different shapes of the power spectrum of the primordial curvature perturbation with the current sensitivity of pulsar timing arrays.

##### 5.Weak gravitational lensing by an ESTGB black hole in the presence of a plasma

**Authors:**Qian Li, Yu Zhang, Zhi-Wen Lin, Qi-Quan Li, Qi Sun

**Abstract:** This paper is devoted to studying the weak-field gravitational lensing properties of a 4D ESTGB black hole, which is surrounded by the plasma medium. The effects of the magnetic charges and the three plasma distribution models in the deflection of light around a 4D ESTGB black hole are investigated in detail. We find that the uniform plasma leads to a larger deflection of light rays in comparison with the singular isothermal sphere (SIS), the non-singular isothermal sphere (NSIS) models. Moreover, the deflection angle increases slightly as the absolute value of the magnetic charge decreases. Finally, we analyze the total magnification of image due to weak gravitational lensing around the black hole. The result shows that the presence of a uniform plasma medium remarkably enhances the total magnification whereas the non-uniform plasma reduces the total magnification.

##### 6.Tracking the Long-Term GW Phase Evolution for HM Cancri-like Binaries with LISA

**Authors:**Naoki Seto

**Abstract:** From prolonged X-ray and optical data of the ultra-compact binary HM Cancri, two groups recently measured the second derivative of its orbital frequency. The space gravitational wave (GW) detector LISA will detect $\sim10^4$ Galactic binaries and their second frequency derivatives will be interesting observational targets for LISA. Here, we forecast the GW signal analysis for HM Cancri, as an ideal reference system for these numerous binaries. We find that, in its nominal operation period $T\sim4$yr, LISA is unlikely to realize a sufficient measurement precision for the reported second frequency derivative of this binary. However, because of a strong dependence on the time baseline, the precision will be drastically improved by extending the operation period of LISA or combining it with other missions (e.g., Taiji and TianQin) in a sequential order.

##### 7.Thermal fluctuation, deflection angle and greybody factor of a high-dimensional Schwarzschild black hole in STVG

**Authors:**Qian Li, Yu Zhang, Qi-Quan Li, Qi Sun

**Abstract:** In this work, we study the thermal fluctuation, deflection angle and greybody factor of the high-dimensional Schwarzschild black hole in scalar-tensor-vector gravity (STVG). Based on the correction of black hole entropy due to thermal fluctuation, we calculate some thermodynamic quantities associated with the correction of black hole entropy. The influence of the first-order and second-order corrections, spacetime dimensionality and STVG parameters on these thermodynamics quantities are discussed in detail. Additionally, by utilizing the Gauss-Bonnet theorem, the deflection angle is obtained in the weak field limit and the effect of two parameters on the results is visualized. Finally, we calculate the bounds on greybody factors of a massless scalar field.

##### 8.First law of thermodynamics and entropy of FLRW universe in modified gravity

**Authors:**Lorenzo Sebastiani

**Abstract:** We investigate the first law of thermodynamics and entropy associated to the apparent horizon of (non-flat) FLRW space-time in different theories of modified gravity and in the presence of a perfect fluid of matter. We pose our attention on those theories which lead to second order differential field equations on FLRW background. In this way, we observe that one may obtain a formula for entropy in terms of the radius of the apparent horizon only. Thus, when considering a modification to the area law of General Relativity, it is possible to reconstruct the gravitational lagrangian consistent with the corresponding first law.

##### 9.Hairy Kiselev Black Hole Solutions

**Authors:**Yaghoub Heydarzade, Maxim Misyura, Vitalii Vertogradov

**Abstract:** In the realm of astrophysics, black holes exist within non-vacuum cosmological backgrounds, making it crucial to investigate how these backgrounds influence the properties of black holes. In this work, we first introduce a novel static spherically-symmetric exact solution of Einstein field equations representing a surrounded hairy black hole. This solution represents a generalization of the hairy Schwarzschild solution recently derived using the extended gravitational decoupling method. Then, we discuss how the new induced modification terms attributed to the primary hairs and various background fields affect the geodesic motion in comparison to the conventional Schwarzschild case. Although these modifications may appear insignificant in most cases, we identify specific conditions where they can be comparable to the Schwarzschild case for some particular background fields.

##### 10.M1 neutrino transport within the numerical-relativistic code BAM with application to low mass binary neutron star mergers

**Authors:**Federico Schianchi, Henrique Gieg, Vsevolod Nedora, Anna Neuweiler, Maximiliano Ujevic, Mattia Bulla, Tim Dietrich

**Abstract:** Neutrino interactions are essential for an accurate understanding of the binary neutron star merger process. In this article, we extend the code infrastructure of the well-established numerical-relativity code BAM that until recently neglected neutrino-driven interactions. In fact, while previous work allowed already the usage of nuclear-tabulated equations of state and employing a neutrino leakage scheme, we are moving forward by implementing a first-order multipolar radiation transport scheme (M1) for the advection of neutrinos. After testing our implementation on a set of standard scenarios, we apply it to the evolution of four low-mass binary systems, and we perform an analysis of ejecta properties. We also show that our new ejecta analysis infrastructure is able to provide numerical relativity-informed inputs for the codes $\texttt{POSSIS}$ and $\texttt{Skynet}$, for the computation of kilonova lightcurves and nucleosynthesis yields, respectively.

##### 11.Scalar fields with derivative coupling to curvature in the Palatini and the metric formulation

**Authors:**Hamed Bouzari Nezhad, Syksy Rasanen

**Abstract:** We study models where a scalar field has derivative and non-derivative couplings to the Ricci tensor and the co-Ricci tensor with a view to inflation. We consider both the metric formulation and the Palatini formulation. In the Palatini case, the couplings to the Ricci tensor and the Ricci scalar give the same result regardless of whether the connection is left general or the non-metricity or the torsion is assumed to vanish. When the co-Ricci tensor is included, the general case and the zero torsion case are physically different. We reduce all the actions to the Einstein frame with minimally coupled matter, and find the leading order differences between the metric case and the Palatini cases.

##### 12.On the Generalized Uncertainty Principle and Cosmology

**Authors:**Oscar López-Aguayo, J. C. López-Domínguez, M. Sabido

**Abstract:** In this work we study the effects of the generalized uncertainty principle (GUP) in cosmology. We start with the Friedmann-Robertson-Walker (FRW) model endowed with a scalar field. After introducing the GUP modification to the model, we solve for the quantum and classical cases. Finally we find the GUP modified Friedmann equations.

##### 13.Particle production from non-minimal coupling in a symmetry breaking potential transporting vacuum energy

**Authors:**Alessio Belfiglio, Youri Carloni, Orlando Luongo

**Abstract:** We propose an inflationary scenario where the inflaton field is non-minimally coupled to spacetime curvature and inflation is driven by a vacuum energy symmetry breaking potential without specifying \emph{a priori} whether the inflaton field is small or large. As we incorporate vacuum energy into our analysis, we further explore the implications of a non-zero potential offset in relation to the emergence of inflationary dynamics. Thus, we propose that vacuum energy can transform into particles as a result of the transition triggered by spontaneous symmetry breaking. This entails a vacuum energy cancellation that yields an effective cosmological constant during inflation by virtue of a quasi-de Sitter evolution and shows that the vacuum energy contribution can manifest as \emph{geometric particles} produced by inflaton fluctuations, with particular emphasis on super-Hubble modes. We conjecture these particles as \emph{quasi-particles} arising from interaction between the inflaton and spacetime geometry, enhanced by non-minimal coupling. Specifically, we propose that dark matter arises from a pure geometric quasi-particle contribution, and we quantify the corresponding dark matter candidate ranges of mass. In this scenario, we further find that a zero potential offset leads to a bare cosmological constant at the end of inflation, while a negative offset would require an additional kinetic (or potential) contribution in order to be fully-canceled. In this regard, we conclude that the scenario of large field inflaton is preferred since it necessitates a more appropriate selection of the offset. Our conclusion is reinforced as small field inflaton would lead to a significant screening of the Newtonian gravitational constant as inflation ends.

##### 14.Geometric post-Newtonian description of massive spin-half particles in curved spacetime

**Authors:**Ashkan Alibabei, Philip K. Schwartz, Domenico Giulini

**Abstract:** We consider the Dirac equation coupled to an external electromagnetic field in curved four-dimensional spacetime with a given timelike worldline $\gamma$ representing a classical clock. We use generalised Fermi normal coordinates in a tubular neighbourhood of $\gamma$ and expand the Dirac equation up to, and including, the second order in the dimensionless parameter given by the ratio of the geodesic distance to the radii defined by spacetime curvature, linear acceleration of $\gamma$, and angular velocity of rotation of the employed spatial reference frame along $\gamma$. With respect to the time measured by the clock $\gamma$, we compute the Dirac Hamiltonian to that order. On top of this `weak-gravity' expansion we then perform a post-Newtonian expansion up to, and including, the second order of $1/c$, corresponding to a `slow-velocity' expansion with respect to $\gamma$. As a result of these combined expansions we give the weak-gravity post-Newtonian expression for the Pauli Hamiltonian of a spin-half particle in an external electromagnetic field. This extends and partially corrects recent results from the literature, which we discuss and compare in some detail.

##### 1.Extending black-hole remnant surrogate models to extreme mass ratios

**Authors:**Matteo Boschini, Davide Gerosa, Vijay Varma, Cristobal Armaza, Michael Boyle, Marceline S. Bonilla, Andrea Ceja, Yitian Chen, Nils Deppe, Matthew Giesler, Lawrence E. Kidder, Guillermo Lara, Oliver Long, Sizheng Ma, Keefe Mitman, Peter James Nee, Harald P. Pfeiffer, Antoni Ramos-Buades, Mark A. Scheel, Nils L. Vu, Jooheon Yoo

**Abstract:** Numerical-relativity surrogate models for both black-hole merger waveforms and remnants have emerged as important tools in gravitational-wave astronomy. While producing very accurate predictions, their applicability is limited to the region of the parameter space where numerical-relativity simulations are available and computationally feasible. Notably, this excludes extreme mass ratios. We present a machine-learning approach to extend the validity of existing and future numerical-relativity surrogate models toward the test-particle limit, targeting in particular the mass and spin of post-merger black-hole remnants. Our model is trained on both numerical-relativity simulations at comparable masses and analytical predictions at extreme mass ratios. We extend the gaussian-process-regression model NRSur7dq4Remnant, validate its performance via cross validation, and test its accuracy against additional numerical-relativity runs. Our fit, which we dub NRSur7dq4EmriRemnant, reaches an accuracy that is comparable to or higher than that of existing remnant models while providing robust predictions for arbitrary mass ratios.

##### 2.Constraining Snyder and GUP models with low-mass stars

**Authors:**Anna Pachoł, Aneta Wojnar

**Abstract:** We investigate the application of an equation of state that incorporates corrections derived from the Snyder model (and the Generalized Uncertainty Principle) to describe the behavior of matter in a low-mass star. Remarkably, the resulting equations exhibit striking similarities to those arising from modified Einstein gravity theories. By modeling matter with realistic considerations, we are able to more effectively constrain the theory parameters, surpassing the limitations of existing astrophysical bounds. The bound we obtain is $\beta_0 \leq 1.36 \times 10^{48}$. We underline the significance of realistic matter modeling in order to enhance our understanding of effects arising in quantum gravity phenomenology and implications of quantum gravitational corrections in astrophysical systems.

##### 3.Fock quantization of a Klein-Gordon field in the interior geometry of a nonrotating black hole

**Authors:**Jerónimo Cortez, Beatriz Elizaga Navascués, Guillermo A. Mena Marugán, Alvaro Torres-Caballeros, José M. Velhinho

**Abstract:** We study the canonical quantization of a scalar field in a Kantowski-Sachs spacetime. For simplicity, we consider compactified spatial sections, since this does not affect the ultraviolet behavior. A time-dependent canonical transformation is performed prior to quantization. As in previously studied cases, the purpose of this canonical transformation is to identify and extract the background contribution to the field evolution which is obstructing a unitary implementation of the field dynamics at the quantum level. This splitting of the time dependence into a background piece and the part to be seen as true quantum evolution is to a large extent determined by the unitarity requirement itself. The quantization is performed in the usual setup of Fock representations, demanding the preservation of the spatial symmetries. Under the joint requirements of quantum unitary dynamics and compatibility with those classical symmetries, the quantization is shown to be unique, in the sense that any two representations with these properties are unitarily equivalent. This confirms the validity of our conditions as criteria to discriminate among possibly inequivalent quantum descriptions. The interest of this analysis goes beyond cosmological applications since the interior of a nonrotating black hole has a geometry of the Kantowski-Sachs type.

##### 4.Swarm-intelligent search for gravitational waves from eccentric binary mergers

**Authors:**Souradeep Pal, K Rajesh Nayak

**Abstract:** We implement an eccentric search for compact binary mergers based on particle swarm optimization. The orbital eccentricity is an invaluable input for understanding the formation scenarios of the binary mergers and can play a pivotal role in finding their electromagnetic counterparts. Current modelled searches rely on pre-computed template banks that are computationally expensive and resistant towards expanding the search parameter space dimensionality. On the other hand, particle swarm optimization offers a straightforward algorithm that dynamically selects template points while exploring an arbitrary dimensional parameter space. Through extensive evaluation using simulated signals from spin-aligned eccentric binary mergers, we discovered that the search exhibits a remarkable autonomy in capturing the effects of both eccentricity and spin. We describe our search pipeline and revisit some of the merger candidates from the gravitational wave transient catalogs.

##### 1.Semianalytic Sensitivity Estimates for Catalogs of Gravitational-Wave Transients

**Authors:**Reed Essick

**Abstract:** I investigate the sensitivity of gravitational-wave searches by analyzing the response of matched filters in stationary Gaussian noise. In particular, I focus on the ability to analytically model the distribution of observed filter responses maximized over coalescence phase and/or a template bank as well as the response of statistics defined for a network of detectors. Semianalytic sensitivity estimates derived assuming stationary Gaussian noise are compared to sensitivity estimates obtained from real searches processing real noise, which is neither perfectly stationary nor perfectly Gaussian. I find that semianalytic estimates are able to reproduce real search sensitivity for the LIGO-Virgo-KAGRA Collaboration's third observing run with high fidelity. I also discuss how to select computational speed-ups (hopeless signal-to-noise ratio cuts) and make predictions for the fourth observing run using projected detector sensitivities.

##### 2.Response of an Interferometer Mounted on an Elastic Square Plate to Gravitational Waves

**Authors:**Thomas Spanner, Thomas Mieling, Stefan Palenta

**Abstract:** Laser-interferometric gravitational wave detectors are commonly modeled as being at rest in transverse-traceless coordinates (and thus geodesic). In this paper, we analyze what happens if the interferometer is mounted on a material that can undergo elastic oscillations caused by the gravitational wave. We thus compute the response of a two-dimensional elastic material to linearized gravitational radiation and compute the resulting response of a laser interferometer, mounted on such a plate.

##### 3.On the degrees of freedom of gravitational radiation with positive cosmological constant

**Authors:**Francisco Fernández-Álvarez

**Abstract:** Results on the isolation of the radiative degrees of freedom of the gravitational field with a positive cosmological constant in full General Relativity are put forward. Methods employed in a recent geometric characterisation of gravitational radiation are used and, inspired by Ashtekar's work on asymptotically flat space-times, a space of connections is defined. Ground differences emerge due to the space-like character of the conformal boundary, and one has to put into play a fundamental result by Friedrich concerning the initial value problem for space-times with a positive cosmological constant. Based on this, half of the radiative degrees of freedom are identified; remarkably, they utterly determine the gravitational radiation content for space-times with algebraically special rescaled Weyl tensor at infinity. Directions for defining the phase space in the general case are proposed.

##### 4.Palatini $F(R,X)$: a new framework for inflationary attractors

**Authors:**Christian Dioguardi, Antonio Racioppi

**Abstract:** Palatini $F(R)$ gravity proved to be a powerful tool in order to realize asymptotically flat inflaton potentials. Unfortunately, it also inevitably implies higher-order inflaton kinetic terms in the Einstein frame that might jeopardize the evolution of the system out of the slow-roll regime. We prove that a $F(R-X)$ gravity, where $X$ is the inflaton kinetic term, solves the issue. Moreover, when $F$ is a quadratic function such a choice easily leads to a new class of inflationary attractors, fractional attractors, that generalizes the already well-known polynomial $\alpha$-attractors.

##### 5.Multi-scale hierarchy from multidimensional gravity

**Authors:**Kirill A. Bronnikov, Arkady A. Popov, Sergey G. Rubin

**Abstract:** We discuss the way of solving the hierarchy problem. We show that starting at the Planck scale, the three energy scales -- inflationary, electroweak and the cosmological ones can be restored. The formation of small parameters is proposed that leads to a successful solution of the problem. The tools involved in the process are $f(R)$ gravity and inhomogeneous extra dimensions. Slow rolling of a space domain from the Planck scale down to the inflationary one gives rise to three consequences: an infinite set of causally disconnected domains (pocket universes) are nucleated; quantum fluctuations in each domain produce a variety of different fields and an extra-dimensional metric distribution; these distributions are stabilized at a sufficiently low energy scale.

##### 6.New Inequalities in Extended Black Hole Thermodynamics

**Authors:**Masaya Amo, Antonia M. Frassino, Robie A. Hennigar

**Abstract:** We propose novel thermodynamic inequalities that apply to stationary asymptotically Anti-de Sitter (AdS) black holes. These inequalities incorporate the thermodynamic volume and refine the reverse isoperimetric inequality. To assess the validity of our conjectures, we apply them to a wide range of analytical black hole solutions, observing compelling evidence in their favour. Intriguingly, our findings indicate that these inequalities may also apply for black holes of non-spherical horizon topology, as we show their validity as well for thin black rings in AdS.

##### 7.A Kerr-Newman-MOG black hole's impact on the magnetic reconnection

**Authors:**Sanjar Shaymatov, Mirzabek Alloqulov, Bobomurat Ahmedov, Anzhong Wang

**Abstract:** In this paper, we study the magnetic reconnection process of energy extraction from a rapidly rotating Kerr-Newman-MOG black hole by investigating the combined effect of black hole charge and the MOG parameter. We explore the energy efficiency of energy extraction and power. Based on an attractive gravitational charge of the MOG parameter $\alpha$ that physically manifests to strengthen black hole gravity we show that the combined effect of the MOG parameter and black hole charge can play an increasingly important role and accordingly lead to high energy efficiency and power for the energy extraction via the magnetic reconnection. Further, we study to estimate the rate of energy extraction under the fast magnetic reconnection by comparing the power of the magnetic reconnection and Blandford-Znajek (BZ) mechanisms. We show that the rate of energy extraction increases as a consequence of the combined effect of black hole charge and MOG parameter. It suggests that magnetic reconnection is significantly more efficient than BZ. In fact, the magnetic reconnection is fueled by magnetic field energy due to the twisting of magnetic field lines around the black hole for the plasma acceleration, and thus MOG parameter gives rise to even more fast spin that can strongly change the magnetic field reconfiguration due to the frame dragging effect. This is how energy extraction is strongly enhanced through the magnetic reconnection, thus making the energy extraction surprisingly more efficient for the Kerr-Newman-MOG black hole than Kerr black hole under the combined effect of black hole charge and MOG parameter.

##### 8.Quasiperiodic oscillations around hairy black holes in Horndeski gravity

**Authors:**Javlon Rayimbaev, Konstantinos F. Dialektopoulos, Furkat Sarikulov, Ahmadjon Abdujabbarov

**Abstract:** Testing gravity theories and their parameters using observations is an important issue in relativistic astrophysics. In this context, we investigate the motion of test particles and their harmonic oscillations in the spacetime of non-rotating hairy black holes (BHs) in Hordeski gravity, together with astrophysical applications of quasiperiodic oscillations (QPOs). We show possible values of upper and lower frequencies of twin-peak QPOs which may occur in the orbits from innermost stable circular orbits to infinity for various values of the Horndeski parameter $q$ in relativistic precession, warped disk models, and three different sub-models of the epicyclic resonant model. We also study the behaviour of the QPO orbits and their position relative to innermost stable circular orbits (ISCOs) with respect to different values of the parameter $q$. {It is obtained that at a critical value of the Horndeski parameter ISCO radius takes $6M$ which has been in the pure Schwarzschild case.} Finally, we obtain mass constraints of the central BH of microquasars GRS 1915+105 and XTE 1550-564 at the GR limit and the possible value of the Horndeski parameter in the frame of the above-mentioned QPO models. The analysis of orbits of twin peak QPOs with the ratio of upper and lower frequencies 3:2, around the BHs in the frame of relativistic precession (RP) and epicyclic resonance (ER4) QPO models have shown that the orbits locate close to the ISCO. The distance between QPO orbits and ISCO is obtained to be less than the error of the observations.

##### 9.Nonlinear dynamics of hot, cold and bald Einstein-Maxwell-scalar black holes in AdS spacetime

**Authors:**Qian Chen, Zhuan Ning, Yu Tian, Bin Wang, Cheng-Yong Zhang

**Abstract:** We investigate the dynamical transition processes of an Einstein-Maxwell-scalar gravitational system between two local ground states and an excited state in the anti-de Sitter spacetime. From the linear perturbation theory, only the excited state possesses a single unstable mode, indicating the dynamical instability. Such an instability is associated with the tachyonic instability due to the presence of an effective potential well near the event horizon. From the nonlinear dynamics simulation, through the scalar field accretion mechanism, the critical phenomena in the transition process of the gravitational system between the two local ground states are revealed. The threshold of the accretion strength indicates the existence of a dynamical barrier in this transition process, which depends on the coupling strength between the scalar and Maxwell fields. On the other hand, for the unstable excited state, there exists a special kind of critical dynamics with a zero threshold for the perturbation strength. The perturbations of different signs push the gravitational system to fall into different local ground states. Interestingly, in an extended parameter space, there exist specific parameters such that the perturbations of non-zero amplitude fail to trigger the single unstable mode of the excited state.

##### 10.Particle production during Inflation with a non-minimally coupled spectator scalar field

**Authors:**Zhe Yu, Chengjie Fu, Zong-Kuan Guo

**Abstract:** We study the inflationary model with a spectator scalar field $\chi$ coupled to both the inflaton and Ricci scalar. The interaction between the $\chi$ field and the gravity, denoted by $\xi R\chi^2$, can trigger the tachyonic instability of certain modes of the $\chi$ field. As a result, the $\chi$ field perturbations are amplified and serve as a gravitational wave (GW) source. When considering the backreaction of the $\chi$ field, an upper bound on the coupling parameter $\xi$ must be imposed to ensure that inflation does not end prematurely. In this case, we find that the inflaton's evolution experiences a sudden slowdown due to the production of $\chi$ particles, resulting in a unique oscillating structure in the power spectrum of curvature perturbations at specific scales. Moreover, the GW signal induced by the $\chi$ field is more significant than primordial GWs at around its peak scale, leading to a noticeable bump in the overall energy spectrum of GWs.

##### 11.Tidal disruption of white dwarfs in a modified gravity theory with SPH

**Authors:**Debojyoti Garain, Pritam Banerjee, Shaswata Chowdhury, Tapobrata Sarkar

**Abstract:** Low energy imprints of modifications to general relativity are often found in pressure balance equations inside stars. These modifications are then amenable to tests via astrophysical phenomena, using observational effects in stellar astrophysics that crucially depend on such equations. One such effect is tidal disruption of stars in the vicinity of black holes. In this paper, using a numerical scheme modelled with smoothed particle hydrodynamics, we study real time tidal disruption of a class of white dwarfs by intermediate-mass black holes, in the low energy limit of a theory of modified gravity that alters the internal physics of white dwarfs, namely the Eddington inspired Born-Infeld theory. In this single parameter extension of general relativity, the mass-radius relation of white dwarfs as well as their tidal disruption radius depend on the modified gravity parameter, and these capture the effect of modifications to general relativity. Our numerical simulations incorporating these show that departure from general relativity in these scenarios might be observationally significant, and should therefore be contrasted with data. In particular, we study observationally relevant physical quantities, i.e., tidal kick velocity and trajectory deviation of the remnant core and fallback rates of the tidal debris in this theory and compare them to the Newtonian limit of general relativity. We also comment on the qualitative differences between the modified gravity theory and one with stellar rotation.

##### 12.Chaos in a tunneling universe

**Authors:**Martin Bojowald, Ari Gluckman

**Abstract:** A recent quasiclassical description of a tunneling universe model is shown to exhibit chaotic dynamics by an analysis of fractal dimensions in the plane of initial values. This result relies on non-adiabatic features of the quantum dynamics, captured by new quasiclassical methods. Chaotic dynamics in the early universe, described by such models, implies that a larger set of initial values of any large expanding branch can be probed.

##### 13.Spherically symmetric elastic bodies in general relativity

**Authors:**Artur Alho, José Natário, Paolo Pani, Guilherme Raposo

**Abstract:** The purpose of this review it to present a renewed perspective of the problem of self-gravitating elastic bodies under spherical symmetry. It is also a companion to the papers [Phys. Rev. D105, 044025 (2022)], [Phys. Rev. D106, L041502 (2022)], and [arXiv:2306.16584 [gr-qc]], where we introduced a new definition of spherically symmetric elastic bodies in general relativity, and applied it to investigate the existence and physical viability, including radial stability, of static self-gravitating elastic balls. We focus on elastic materials that generalize fluids with polytropic, linear, and affine equations of state, and discuss the symmetries of the energy density function, including homogeneity and the resulting scale invariance of the TOV equations. By introducing invariant characterizations of physical admissible initial data, we numerically construct mass-radius-compactness diagrams, and conjecture about the maximum compactness of stable physically admissible elastic balls.

##### 14.Epicyclic frequencies in the equatorial plane around stationary and axially symmetric wormhole geometries

**Authors:**Vittorio De Falco

**Abstract:** Epicyclic frequencies are usually observed in X-ray binaries and constitute a powerful astrophysical mean to probe the strong gravitational field around a compact object. We consider them in the equatorial plane around a general stationary and axially symmetric wormhole. We first search for the wormholes' existence, distinguishing them from a Kerr black hole. Once there will be available observational data on wormholes, we present a strategy to reconstruct the related metrics. Finally, we discuss the implications of our approach and outline possible future perspectives.

##### 15.On the approximate relation between black-hole perturbation theory and numerical relativity

**Authors:**Tousif Islam, Gaurav Khanna

**Abstract:** We investigate the interplay between numerical relativity (NR) and point-particle black hole perturbation theory (ppBHPT) in the comparable mass regime. Specifically, we reassess the $\alpha$-$\beta$ scaling technique, previously introduced by Islam et al, as a means to effectively match ppBHPT waveforms to NR waveforms within this regime. Utilizing publicly available long NR data for a mass ratio of $q=3$ (where $q:=m_1/m_2$ represents the mass ratio of the binary, with m_1 and m_2 denoting the masses of the primary and secondary black holes, respectively), encompassing the final $\sim 65$ orbital cycles of the binary evolution, we examine the range of applicability of such scalings. We observe that the scaling technique remains effective even during the earlier stages of the inspiral. Additionally, we provide commentary on the temporal evolution of the $\alpha$ and $\beta$ parameters and discuss whether they can be approximated as constant values. Consequently, we derive the $\alpha$-$\beta$ scaling as a function of orbital frequencies and demonstrate that it is equivalent to a frequency-dependent correction. We further provide a brief comparison between Post-Newtonian waveform and the rescaled ppBHPT waveform at $q=3$ and comment on their regime of validity. Finally, we explore the possibility of using PN to obtain the $\alpha$-$\beta$ calibration parameters and still provide a rescaled ppBHPT waveform that matches NR.

##### 16.New Type of Traversable Wormhole

**Authors:**Frans R. Klinkhamer

**Abstract:** We review a new traversable-wormhole solution of the gravitational field equation of general relativity without exotic matter. Instead of having exotic matter to keep the wormhole throat open, the solution relies on a 3-dimensional "spacetime defect," which is characterized by a locally vanishing metric determinant. We also discuss the corresponding multiple-vacuum-defect-wormhole solution and possible experimental signatures from a "gas" of vacuum-defect wormholes. Multiple vacuum-defect wormholes appear to allow for backward time travel.

##### 17.Induced Gravitational Waves from Ultra Slow-Roll Inflation and Pulsar Timing Arrays Observations

**Authors:**Hassan Firouzjahi, Alireza Talebian

**Abstract:** The stochastic gravitational wave background (SGWB) detected recently by the pulsar timing arrays (PTAs) observations may have cosmological origins. In this work we consider a model of single field inflation containing an intermediate phase of ultra slow-roll. Fixing the amplitude of the peak of curvature perturbations by the PBHs bounds we calculate the gravitational waves (GWs) induced from the curvature perturbations enhanced during USR. The spectrum of the induced GWs depends on the sharpness of the transition from the USR phase to the final attractor phase as well as to the duration of the USR period. While the model can accommodate the current PTAs data but it has non-trivial predictions for the induced GWs on higher frequency ranges which can be tested by future observations.

##### 18.On the maximum mass and oblateness of rotating neutron stars with generic equations of state

**Authors:**Carlo Musolino, Christian Ecker, Luciano Rezzolla

**Abstract:** A considerable effort has been dedicated recently to the construction of generic equations of state (EOSs) for matter in neutron stars. The advantage of these approaches is that they can provide model-independent information on the interior structure and global properties of neutron stars. Making use of more than $10^6$ generic EOSs, we asses the validity of quasi-universal relations of neutron star properties for a broad range of rotation rates, from slow-rotation up to the mass-shedding limit. In this way, we are able to determine with unprecedented accuracy the quasi-universal maximum-mass ratio between rotating and nonrotating stars and reveal the existence of a new relation for the surface oblateness, i.e., the ratio between the polar and equatorial proper radii. We discuss the impact that our findings have on the imminent detection of new binary neutron-star mergers and how they can be used to set new and more stringent limits on the maximum mass of nonrotating neutron stars, as well as to improve the modelling of the X-ray emission from the surface of rotating stars.

##### 1.Geometrically thick equilibrium tori around a dyonic black hole with quasi-topological electromagnetism

**Authors:**Xuan Zhou, Songbai Chen, Jiliang Jing

**Abstract:** We study the geometrically thick non-self gravitating equilibrium tori orbiting the static spherically symmetric dyonic black hole with quasi-topological electromagnetic electromagnetism. Our results show that the electric and magnetic charges together with the coupling parameter in the quasi-topological electromagnetic electromagnetism lead to a much richer class of equilibrium tori. There is a range of parameters which allows for the existence of double tori. The properties of the double equilibrium tori and the accretion in the double tori become far richer. Moreover, the transitions between single torus and double tori solutions can occur by changing the specific angular momentum of the fluid. These richer properties of equilibrium tori could help to understand the dyonic black hole and its thick accretion disk.

##### 2.Quantum system ascribed to the Oppenheimer-Snyder model of massive star

**Authors:**A. Góźdź, J. J. Ostrowski, A. Pȩdrak, W. Piechocki

**Abstract:** We quantize the Oppenheimer-Snyder model of black hole using the integral quantization method. We treat spatial and temporal coordinates on the same footing both at classical and quantum levels. Our quantization resolves or smears the singularities of the classical curvature invariants. Quantum trajectories with bounces can replace singular classical ones. The considered quantum black hole may have finite lifetime. As a byproduct, we obtain the resolution of the gravitational singularity of the Schwarzschild black hole at quantum level.

##### 3.Multipole tidal effects in the gravitational-wave phases of compact binary coalescences

**Authors:**Tatsuya Narikawa

**Abstract:** We present the component form of the multipole tidal phase for the gravitational waveform of compact binary coalescences (MultipoleTidal), which consists of the mass quadrupole, the current quadrupole, and the mass octupole moments. We demonstrate the phase evolution and the phase difference between the tidal multipole moments (MultipoleTidal) and the mass quadrupole (PNTidal) as well as the numerical-relativity calibrated model (NRTidalv2). We find the MultipoleTidal gives a larger phase shift than the PNTidal, and is closer to the NRTidalv2. We compute the matches between waveform models to see the impact of the tidal multipole moments on the gravitational wave phases. We find the MultipoleTidal gives larger matches to the NRTidalv2 than the PNTidal, in particular, for high masses and large tidal deformabilities. We also apply the MultipoleTidal model to binary neutron star coalescence events GW170817 and GW190425. We find that the current quadrupole and the mass octupole moments give no significant impact on the inferred tidal deformability.

##### 4.Parameter estimation for Einstein-dilaton-Gauss-Bonnet gravity with ringdown signals

**Authors:**Cai-Ying Shao, Yu Hu, Cheng-Gang Shao

**Abstract:** Future space-based gravitational-wave detectors will detect gravitational waves with high sensitivity in the millihertz frequency band, which provides more opportunities to test theories of gravity than ground-based ones. The study of quasinormal modes (QNMs) and their application to testing gravity theories have been an important aspect in the field of gravitational physics. In this study, we investigate the capability of future space-based gravitational wave detectors such as LISA, TaiJi, and TianQin to constrain the dimensionless deviating parameter for Einstein-dilaton-Gauss-Bonnet (EdGB) gravity with ringdown signals from the merger of binary black holes. The ringdown signal is modeled by the two strongest QNMs in EdGB gravity. Taking into account time-delay interferometry, we calculate the signal-to-noise ratio (SNR) of different space-based detectors for ringdown signals to analyze their capabilities. The Fisher information matrix is employed to analyze the accuracy of parameter estimation, with particular focus on the dimensionless deviating parameter for EdGB gravity. The impact of the parameters of gravitational wave sources on the estimation accuracy of the dimensionless deviating parameter has also been studied. We find that the constraint ability of EdGB gravity is limited because the uncertainty of the dimensionless deviating parameter increases with the decrease of the dimensionless deviating parameter. LISA and TaiJi has more advantages to constrain the dimensionless deviating parameter to a more accurate level for the massive black hole, while TianQin is more suitable for less massive black holes. Bayesian inference method is used to perform parameter estimation on simulated data, which verifies the reliability of the conclusion.

##### 5.Anisotropic Inflation in Dipolar Bose-Einstein Condensates

**Authors:**Arun Rana, Abhijit Pendse, Sebastian Wüster, Sukanta Panda

**Abstract:** Early during the era of cosmic inflation, rotational invariance may have been broken, only later emerging as a feature of low-energy physics. This motivates ongoing searches for residual signatures of anisotropic space-time, for example in the power spectrum of the cosmic microwave background. We propose that dipolar Bose-Einstein condensates (BECs) furnish a laboratory quantum simulation platform for the anisotropy evolution of fluctuation spectra during inflation, exploiting the fact that the speed of dipolar condensate sound waves depends on direction. We construct the anisotropic analogue space-time metric governing sound, by linking the time-varying strength of dipolar and contact interactions in the BEC to the scale factors in different coordinate directions. Based on these, we calculate the dynamics of phonon power spectra during an inflation that renders the initially anisotropic universe isotropic. We find that the expansion speed provides an experimental handle to control and study the degree of final residual anisotropy. Gravity analogues using dipolar condensates can thus provide tuneable experiments for a field of cosmology that was until now confined to a single experiment, our universe.

##### 6.Inflation in simple one-loop effective potentials of perturbative quantum gravity

**Authors:**A. Arbuzov, D. Kuznetsov, B. Latosh, V. Shmidt

**Abstract:** We study inflation in scalar-tensor perturbative quantum gravity driven by a one-loop effective potential. We consider effective potentials generated by three models. The first model describes a single scalar field with a non-vanishing mass. The second model describes a massless scalar field with non-minimal coupling to the Einstein tensor. The third model describes a single scalar field with quadratic and quartic interaction terms. All models develop a small tensor-to-scalar ratio, but the tilt of the scalar spectrum is too large to be consistent with the observational data. We discuss ways to extend these models to account for other quantum effects.

##### 7.Quasinormal modes and stability of higher dimensional rotating black holes under massive scalar perturbations

**Authors:**Kai-Peng Lu, Wenbin Li, Jia-Hui Huang

**Abstract:** We consider the stability of six-dimensional singly rotating Myers-Perry black holes under massive scalar perturbations. Using Leaver's continued fraction method, we compute the quasinormal modes of the massive scalar fields. All modes found are damped under the quasinormal boundary conditions. It is also found that long-living modes called quasiresonances exist for large scalar masses as in the four-dimensional Kerr black hole case. Our numerical results provide a direct and complement evidence for the stability of six-dimensional MP black holes under massive scalar perturbation.

##### 8.Interacting quintessence cosmology from Noether symmetries: comparing theoretical predictions with observational data

**Authors:**Ester Piedipalumbo, Stefano Vignolo, Pasquale Feola, Salvatore Capozziello

**Abstract:** In the framework of scalar-tensor gravity, we consider non-flat interacting quintessence cosmology where a scalar field is interacting with dark matter. Such a scalar field can be a standard or a phantom one. We use the Noether Symmetry Approach to obtain general exact solutions for cosmological equations and to select scalar-field self-interaction potentials. It turns out that the found solutions can reproduce the accelerated expansion of the Universe, and are compatible with observational dataset, as the SNeIa Pantheon data, gamma ray bursts Hubble diagram, and direct measurements of the Hubble parameter.

##### 9.Possible scenario of relic wormhole formation

**Authors:**A. A. Kirillov, E. P. Savelova

**Abstract:** It is shown that in the presence of virtual wormholes, the vacuum is unstable, which leads to a series of phase transitions in the early Universe. Then the standard Kibble scenario predicts the formation of defects such as domain walls. An unusual feature of virtual wormholes is that they generate defects with negative energy density. Such defects have macroscopic dimensions and can support the necks of already real primary wormholes, which gives reason to consider relic wormholes as realistic astrophysical objects.

##### 10.The waveform of the scalar induced gravitational waves in light of Pulsar Timing Array data

**Authors:**Zhu Yi, Qing Gao, Yungui Gong, Yue Wang, Fengge Zhang

**Abstract:** The recent gravitational wave signal detected by NANOGrav, Parkers Pulsar Timing Array, European Pulsar Timing Array, and Chinese Pulsar Timing Array collaborations can be explained by scalar induced secondary gravitational waves. The waveforms of scalar induced secondary gravitational waves exhibit a near-model-independent behavior in the infrared region $k\ll k_p$, $h^2\Omega_\text{GW} = A_\text{GW}\left(k/k_{\rm ref}\right)^{n_{\mathrm{GW}}}$, where the index $n_{\mathrm{GW}}$ is $n_{\mathrm{GW}} = 2 n_1$ for $n_1<3/2$, $n_{\mathrm{GW}} = 3-3/ \ln(k_p/k)$ for $n_1=3/2$, and $n_{\mathrm{GW}} =3-2/ \ln(k_p/k)$ for $n_1>3/2$ if the primordial curvature perturtation is parameterized as a power-law with the index $n_1$. Through Bayesian analysis, we discuss the parameter space that characterizes the behavior of scalar induced gravitational waves in the infrared region. The mean values and one sigma confidence intervals of parameters are $\log_{10} A_\mathrm{GW} = -7.18^{+0.24}_{-0.26}$ and $n_1 = 0.94^{+0.17}_{-0.17}$ for $n_1<3/2$, $\log_{10} A_\mathrm{GW} = -6.96^{+0.27}_{-0.30}$ and $\log_{10} k_p/ {\rm Mpc}^{-1} = 8.24^{+1.48}_{-0.58}$ for $n_1=3/2$, and $\log_{10} A_\mathrm{GW} = -6.77^{+0.19}_{-0.22}$ and $\log_{10} k_p/ {\rm Mpc}^{-1} = 8.37^{+1.69}_{-0.68}$ for $n_1>3/2$. Comparing with the interpretation of the detected signal as stochastic background from massive black hole binaries, the results for $n_1<3/2$, $n_1=3/2$, and $n_1>3/2$ give the support of scalar induced gravitational waves with the Bayes factor $\ln \mathcal{B}= 2.8$, $\ln \mathcal{B}= 2.9$, and $\ln \mathcal{B} = 1.8$, respectively.

##### 11.More Exact Thermodynamics of Nonlinear Charged AdS Black Holes in 4D Critical Gravity

**Authors:**Prosenjit Paul, Sudhaker Upadhyay, Yerlan Myrzakulov, Dharm Veer Singh, Kairat Myrzakulov

**Abstract:** In this paper, we investigate nonlinearly charged AdS black holes in four-dimensional critical gravity and study more exact black hole thermodynamics under the effect of small statistical fluctuations. We compute the correction to the thermodynamics of nonlinearly charged AdS black hole up to the leading order. We discuss the stability of black holes under the circumstances of fluctuation and find that fluctuation causes instability in the black holes. Moreover, both the isothermal and adiabatic compressibilities are also derived. Finally, we estimate the role of small fluctuations on the equation of states and study the $P-v$ diagram of nonlinearly charged AdS black hole.

##### 12.Piercing of a solitonic boson star by a black hole

**Authors:**Zhen Zhong, Vitor Cardoso, Taishi Ikeda, Miguel Zilhão

**Abstract:** Recently, the piercing of a mini boson star by a black hole was studied, with tidal capture and the discovery of a "gravitational atom" being reported ( arXiv:2206.00021 [gr-qc] ). Building on this research, we extend the study by including a hexic solitonic potential and explore the piercing of a solitonic boson star by a black hole. Notably, the solitonic boson star can reach higher compactness, which one might expect could alter the dynamics in this context. Our findings suggest that even when the black hole's size approaches the test particle limit, the solitonic boson star is easily captured by the black hole due to an extreme tidal capture process. Regardless of the black hole initial mass and velocity, our results indicate that over 85% of the boson star material is accreted. Thus, the self-interaction does not alter the qualitative behavior of the system.

##### 13.The weak field limit of quantum matter back-reacting on classical spacetime

**Authors:**Isaac Layton, Jonathan Oppenheim, Andrea Russo, Zachary Weller-Davies

**Abstract:** Consistent coupling of quantum and classical degrees of freedom exists so long as there is both diffusion of the classical degrees of freedom and decoherence of the quantum system. In this paper, we derive the Newtonian limit of such classical-quantum (CQ) theories of gravity. Our results are obtained both via the gauge fixing of the recently proposed path integral theory of CQ general relativity and via the CQ master equation approach. In each case, we find the same weak field dynamics. We find that the Newtonian potential diffuses by an amount lower bounded by the decoherence rate into mass eigenstates. We also present our results as an unravelled system of stochastic differential equations for the trajectory of the hybrid classical-quantum state and provide a series of kernels for constructing figures of merit, which can be used to rule out part of the parameter space of classical-quantum theories of gravity by experimentally testing it via the decoherence-diffusion trade-off. We compare and contrast the weak field limit to previous models of classical Newtonian gravity coupled to quantum systems. Here, we find that the Newtonian potential and quantum state change in lock-step, with the flow of time being stochastic.

##### 14.Spin as a probe of axion physics in general relativity

**Authors:**Yuri N. Obukhov

**Abstract:** The dynamics of spin in external electromagnetic, gravitational, and axion fields is analysed in the framework of the gravitoelectromagnetism approach in Einstein's general relativity theory. We consistently extend the recent studies from the flat Minkowski geometry to the curved spacetime manifolds, contributing to the discussion of the possible new role of a precessing spin as an ``axion antenna'' that can be used to detect the hypothetical axion-like dark matter. The formalism developed helps to clarify the subtle influence of the gravitational/inertial and axion fields in the ultra-sensitive high-energy spin experiments with charged particles and neutrons at accelerators and storage rings devoted to testing fundamental physical symmetries, including attempts to establish the nature of dark matter in the Universe.

##### 15.Quantum Gravitational Corrections to Electromagnetism And Backreaction

**Authors:**Sanjib Katuwal

**Abstract:** This dissertation examines the impact of quantum gravity on electromagnetism and its backreaction, using perturbative general relativity as an effective field theory. Our analysis involves quantum-correcting Maxwell's equations to obtain a gauge-independent, real, and causal effective field equation that describes quantum gravitational effects on electromagnetism. Additionally, we present a perturbative mechanism through which quantum gravity induces a dimension six coupling between a massive scalar and electromagnetism. To investigate the effects of electromagnetism on the gravitational sector, we derive an exact, dimensionally regulated, Fourier mode sum for the Lorentz gauge propagator of a massive photon on an arbitrary cosmological background supported by a scalar inflaton. This allows us to calculate the effective potential induced by photons. Finally, we use a similar Fourier mode sum for a time-dependent mass to study the effective force on the inflaton 0-mode and its impact on reheating.

##### 16.The Motion of Test Bodies around Kerr Black Holes

**Authors:**Adrien Druart

**Abstract:** This thesis aims to explore the properties of the motion of finite size, compact test bodies around a Kerr black hole in the small mass-ratio approximation. The small body is modelled as a perturbation of Kerr geometry, neglecting its gravitational back-reaction but including deviations from a purely geodesic motion by allowing it to possess a non-trivial internal structure. Such a body can be accurately described by a worldline endowed with a collection of multipole moments. Hereafter, we shall always consider the multipole expansion truncated at quadrupole order. Moreover, only spin-induced quadrupole moment will be taken into account, thus discarding the presence of any tidal-type deformation. For astrophysically realistic objects, this approximation is consistent with expanding the equations of motion up to second order in the body's spin magnitude. The text is structured as follows. The first part is devoted to an extended review of geodesic motion in Kerr spacetime, including Hamiltonian formulation and classification of timelike geodesics, with a particular emphasis put on near-horizon geodesics of high spin black holes. The second part introduces the equations of motion for extended test bodies in generic curved spacetime, also known as Mathisson-Papapetrou-Dixon (MPD) equations. The third part discusses conserved quantities for the MPD equations in Kerr spacetime, restricting to the aforementioned quadrupole approximation. Finally, the covariant Hamiltonian formulation of test body motion in curved spacetime is presented, and an Hamiltonian reproducing the spin-induced quadrupole MPD equations is derived. It is shown that the constants of motion obtained in the previous part directly arise while solving the Hamilton-Jacobi equation at first order in the spin magnitude. Some expectations regarding the computation at quadratic order close the discussion.

##### 17.Does extended Chaplygin gas support an emergent universe ?

**Authors:**Rikpratik Sengupta, Prasenjit Paul, B C Paul, M Kalam

**Abstract:** In this paper, we attempt to explore the possibility of a obtaining a viable emergent universe scenario supported by a type of fluid known as the extended Chaplygin gas, which extends a modification to the equation of state of the well known modified Chaplygin gas by considering additional higher order barotropic fluid terms. We consider quadratic modification only. Such a fluid is capable of explaining the present cosmic acceleration and is a possible dark energy candidate. We construct a theoretical model of the emergent universe assuming it is constituted from such a fluid. It interestingly turns out that the theoretical constraints we obtain on the extended Chaplygin gas parameters from our emergent universe model are well in agreement with the observational constraint on these parameters from BICEP2 data. Our model is found to replicate the late time behaviour really well and reproduces $\Lambda$-CDM like behaviour, as evident from the analysis of the statefinder parameters. Moreover, the Hubble parameter analysis shows that for theoretically constrained values of the ECG parameters, the Hubble tension can be resolved yielding higher values of the present Hubble parameter $H_0$ in all possible cases. Also, the value of $H(z)$ at a redshift $z=2.34$ fits better than $\Lambda-CDM$ with recent observations in some cases. This leads us to the realization that such a fluid is not only a probable candidate for dark energy, but also supports an emergent universe unlike modified Chaplygin gas and the initial singularity problem can be resolved in a flat universe within the standard relativistic context.

##### 18.Traversable Lorentzian wormhole on the Shtanov-Sahni braneworld with matter obeying the energy conditions

**Authors:**Rikpratik Sengupta, Shounak Ghosh, M. Kalam

**Abstract:** In this paper we have explored the possibility of constructing a traversable wormhole on the Shtanov-Sahni braneworld with a timelike extra dimension. We find that the Weyl curvature singularity at the throat of the wormhole can be removed with physical matter satisfying the NEC $\rho+p \geq 0$, even in the absence of any effective $\Lambda$-term or any type of charge source on the brane. (The NEC is however violated by the effective matter description on the brane arising due to effects of higher dimensional gravity.) Besides satisfying NEC the matter constituting the wormhole also satisfies the Strong Energy Condition (SEC), $\rho+3p \geq 0$, leading to the interesting possibility that normal matter on the brane may be harnessed into a wormhole. Incidentally, these conditions also need to be satisfied to realize a non-singular bounce and cyclic cosmology on the brane\cite{Sahni4} where both past and future singularities can be averted. Thus, such a cyclic universe on the brane, constituted of normal matter can naturally contain wormholes. The wormhole shape function on the brane with a time-like extra dimension represents the tubular structure of the wormhole spreading out at large radial distances much better than in wormholes constructed in a braneworld with a spacelike extra dimension and have considerably lower mass resulting in minimization of the amount of matter required to construct a wormhole. Wormholes in the Shtanov-Sahni (SS) braneworld also have sufficiently low tidal forces, facilitating traversability. Additionally they are found to be stable and exhibit a repulsive geometry. We are left with the intriguing possibilty that both types of curvature singularity can be resolved with the SS model, which we discuss at the end of the concluding section.

##### 19.Existence of Time-like Geodesics in Asymptotically Flat Spacetimes: A Generalized Topological Criterion

**Authors:**Krish Jhurani, Tyler McMaken

**Abstract:** This paper examines the issue of the existence and nature of time-like geodesics in asymptotically flat spacetimes and proposes a novel generalized topological criterion for the existence of time-like geodesics. Its validity is proved using theorems such as the Jordan-Brouwer Separation Theorem, the Raychaudhuri Equation, and key elements of Differential Geometry. More specifically, the proof primarily hinges on a closed, simply-connected subset of the spacetime manifold and a continuous map, causing a non-trivial induction on the first homology groups, from the boundary of this subset to a unit circle. The mathematical analysis conclusively affirms the presence of these geodesics, intersecting transversally within the said subset of spacetime. Findings underscore these geodesics' significant implications for the structure of asymptotically flat spacetimes, including stability, and hypothetical existence of wormholes. The generalized topological criterion also has implications on the problem of obstructions for the existence of Lorentzian metrics, and Einstein's Constraint Equations. Future research should extend this topological criterion to other classes of spacetimes, including those with non-trivial topologies or non-zero cosmological constants. Also, the criterion's application to study complex dynamical systems, such as gravitational waves or rotating black holes, could offer significant insights.

##### 1.Shadows and photon rings of a spherically accreting Kehagias-Sfetsos black hole

**Authors:**Mohaddese Heydari-Fard, Malihe Heydari-Fard, Nematollah Riazi

**Abstract:** By considering Kehagias-Sfetsos black hole in the framework of the Ho\v{r}ava-Lifshitz gravity, we study the optical appearance of such black holes surrounded by spherical accretion flow. For the static/infalling spherical accretion flow, we compute the observed specific intensity as a function of impact parameter. We also investigate the effect of the Ho\v{r}ava parameter and accreting matter on the luminosity of shadows and photon rings. It is found that an increase in the Ho\v{r}ava parameter decreases the shadow size, while the shadows and photon rings luminosities increase. Moreover, we constrain the Ho\v{r}ava parameter from the observational data reported by the Event Horizon Telescope for M87* and Sgr A*.

##### 2.Sensitivity to anisotropic stochastic gravitational-wave background with space-borne networks

**Authors:**Zheng-Cheng Liang, Zhi-Yuan Li, En-Kun Li, Jian-dong Zhang, Yi-Ming Hu

**Abstract:** This paper explores the detection capability of space-borne detectors to the anisotropic stochastic gravitational-wave background (SGWB) without relying on the low-frequency approximation. To assess the detection performance, we calculate the power-law integrated sensitivity (PLIS) curve. Our results demonstrate that a single detector has limited capabilities in detecting multipole moments beyond the monopole ($l=0$), quadrupole ($l=2$), and hexadecapole ($l=4$). However, when multiple detectors are combined, the presence of multiple pointing directions and the separation between detectors significantly enhance the detection capabilities for the other multipole moments. For instance, when considering the dipole ($l=1$), combining TianQin with TianQin II and LISA with TianQin significantly improves the detection sensitivity by 2-3 orders of magnitude, compared with using a single TianQin and a single LISA, respectively.

##### 3.Thermodynamic phase transition and winding number for the third-order Lovelock black hole

**Authors:**Yu-Shan Wang, Zhen-Ming Xu, Bin Wu

**Abstract:** Phase transition is important for understanding the nature and evolution of the black hole thermodynamic system. In this study, the connection between the phase transition of a black hole and the winding number derived by the complex analysis is used to predict the type of the black hole phase transition. For the third-order Lovelock black holes, at the hyperbolic topology in any dimensions and the spherical topology in $7$ dimensions, we arrive at the winding numbers both are $W=3$ which predicts that the system will undergo both the first-order and second-order phase transitions. For the spherical topology in $7<d<12$ dimensions, the winding number is $W=4$ and the corresponding phase transition will occur in two situations: one with only pure second-order phase transition and the other with both first-order and second-order phase transitions. We further confirm the correctness and rationality of this prediction by placing the black hole thermodynamics system in the potential field.

##### 4.The key role of Lagrangian multiplier in mimetic gravitational theory in the frame of isotropic compact star

**Authors:**G. G. L. Nashed

**Abstract:** Recently, the mimetic gravitational theory has gained much attention in the frame of cosmology as well as in the domain of astrophysics. In this study, we show that in the frame of mimetic gravitation theory we are not able to derive an isotropic model. As a result, our focus shifts towards combining mimetic gravitational theory with the Lagrangian multiplier. The field equations of a static isotropic gravitational system that controls the geometry and dynamics of star structure are studied in the frame of mimetic theory coupled with a Lagrangian multiplier using a non-linear equation of state. An energy density is assumed from where all the other unknowns are fixed and a new isotropic model is derived. The physical analysis of this model is studied from different viewpoints and consistent results compatible with a realistic isotropic star are investigated analytically and graphically. Ultimately, we demonstrate the stability of the model in question by employing the adiabatic index technique.

##### 5.On possible wormhole solutions supported by non-commutative geometry within $f(R, L_m)$ gravity

**Authors:**N. S. Kavya, V. Venkatesha, G. Mustafa, P. K. Sahoo

**Abstract:** Non-commutativity is a key feature of spacetime geometry. The current article explores the traversable wormhole solutions in the framework of $f(R,L_m)$ gravity within non-commutative geometry. By using the Gaussian and Lorentzian distributions, we construct tideless wormholes for the nonlinear $f(R,L_m)$ model $f(R,L_m)=\dfrac{R}{2}+L_m^\alpha$. For both cases, we derive shape functions and discuss the required different properties with satisfying behavior. For the required wormhole properties, we develop some new constraints. The influence of the involved model parameter on energy conditions is analyzed graphically which provides a discussion about the nature of exotic matter. Further, we check the physical behavior regarding the stability of wormhole solutions through the TOV equation. An interesting feature regarding the stability of the obtained solutions via the speed of sound parameters within the scope of average pressure is discussed. Finally, we conclude our results.

##### 6.ICRC2023 Proceedings: Proposal of a gauge-invariant treatment of $l=0,1$-mode perturbations on the Schwarzschild background spacetime

**Authors:**Kouji Nakamura

**Abstract:** A gauge-invariant perturbation theory on a generic background spacetime is developing from 2003 and ``zero-mode problem'' for linear metric perturbations was proposed as the essential problem of this theory. In the perturbation theory on the Schwarzschild background spacetime, $l=0,1$ modes correspond to the above ``zero-mode'' and the gauge-invariant treatments of these modes is a famous non-trivial problem in perturbation theories on the Schwarzschild background spacetime. Due to this situation, a gauge-invariant treatment for these $l=0,1$-mode perturbations is proposed. Through this gauge-invariant treatment, the solutions to the linearized Einstein equation for these modes with a generic matter field are derived. In the vacuum case, the linearized version of uniqueness theorem of Kerr spacetime is confirmed in a gauge-invariant manner. In this sense, our proposal is reasonable.

##### 7.Fully general relativistic simulations of rapidly rotating quark stars: Oscillation modes and universal relations

**Authors:**Kenneth Chen, Lap-Ming Lin

**Abstract:** Numerical simulation of strange quark stars (QSs) is challenging due to the strong density discontinuity at the stellar surface. In this paper, we report successful simulations of rapidly rotating QSs and study their oscillation modes in full general relativity. Building on top of the numerical relativity code \texttt{Einstein Toolkit}, we implement a positivity-preserving Riemann solver and a dust-like atmosphere to handle the density discontinuity at the surface. We demonstrate the robustness of our numerical method by performing stable evolutions of rotating QSs close to the Keplerian limit and extracting their oscillation modes. We focus on the quadrupolar $l=|m|=2$ $f$-mode and study whether they can still satisfy the universal relations recently proposed for rotating neutron stars (NSs). We find that two of the three proposed relations can still be satisfied by rotating QSs. For the remaining broken relation, we propose a new relation to unify the NS and QS data by invoking the dimensionless spin parameter $j$. The onsets of secular instabilities for rotating QSs are also studied by analyzing the $f$-mode frequencies. Same as the result found previously for NSs, we find that QSs become unstable to the Chandrasekhar-Friedman-Schutz instability when the angular velocity of the star $\Omega \approx 3.4 \sigma_0$ for sequences of constant central energy density, where $\sigma_0$ is the mode frequency of the corresponding nonrotating configurations. For the viscosity-driven instability, we find that QSs become unstable when $j\approx 0.881$ for both sequences of constant central energy density and constant baryon mass. Such a high value of $j$ cannot be achieved by realistic rotating NSs before reaching the Keplerian limit.

##### 8.The River Model of Gravitational Collapse

**Authors:**Soumya Chakrabarti

**Abstract:** We show that the transformation of a time-evolving spherically symmetric metric tensor into a Painleve-Gullstrand-Lemaitre form brings forth a few curious consequences. The time evolution describes a non-singular gravitational collapse, leading to a bounce and dispersal of all the clustered matter, or a wormhole geometry for certain initial conditions. The null convergence condition is violated only at the onset of bounce or the wormhole formation. As an example, the requirements to develop a Simpson-Visser wormhole/regular black-hole geometry is discussed. The solution can be regarded as a new time-evolving twin of sonic dumb holes found in analog gravity.

##### 9.On a Schwarzschild-type defect wormhole

**Authors:**Zi-Liang Wang

**Abstract:** We investigate a new type of Schwarzschild wormhole, which relies on a 3-dimensional spacetime defect with degenerate metrics. This particular wormhole is a solution of the vacuum Einstein equations. We also study the generalized Schwarzschild-type defect wormhole and discuss the Null Energy Condition. In particular, we investigate the geodesics and geodesic congruences of the generalized Schwarzschild-type defect wormhole. Additionally, we explore the optical appearance of these wormholes, shedding light on their observable features.

##### 10.On the foundations of entropic cosmologies: inconsistencies, possible solutions and dead end signs

**Authors:**Hussain Gohar, Vincenzo Salzano

**Abstract:** In this letter we explore the foundations of entropic cosmology and highlight some important flaws which have emerged and adopted in the recent literature. We argue that, when applying entropy and temperature on the cosmological horizon by assuming the holographic principle for all thermodynamic approaches to cosmology and gravity, one must derive the consistent thermodynamic quantities following Clausius relation. One key assumption which is generally overlooked, is that in this process one must assume a mass-to-horizon relation, which is generally taken as a linear one. We show that, regardless of the type of entropy chosen on the cosmological horizon, when a thermodynamically consistent corresponding temperature is considered, all modified entropic force models are equivalent to and indistinguishable from the original entropic force models based on standard Bekenstein entropy and Hawking temperature. As such, they are also plagued by the same problems and inability to describe in a satisfactory qualitative and quantitative way the cosmological dynamics as it emerges from the probes we have. We also show that the standard accepted parameterization for Hawking temperature (including a $\gamma$ rescaling) is actually not correctly applied, namely, it is not related to entropy in a thermodynamically consistent way. Finally, we clearly state that the explicit form of the entropic force on cosmological horizons is mostly dictated by the assumption on the mass-to-horizon relation. As such, we discuss what should be done in order to fix all such issues, and what conceptually could be implied by its correct implementation in order to advance in the field.

##### 11.Gravitational collapse of a spherical scalar field

**Authors:**Roberto Giambò

**Abstract:** Examining the relativistic collapse of a spherical spacetime where gravity is coupled with a scalar field, this review provides a thorough analysis of some of the most relevant studies from both analytical and numerical perspectives. The discussion includes achievements made in this field, with a focus on those related to cosmic censorship, as well as recent perspectives on the topic.

##### 12.Realizing late-time cosmology in the context of Dynamical Stability Approach

**Authors:**Anirban Chatterjee, Saddam Hussain, Kaushik Bhattacharya

**Abstract:** We examine the scenario of non-minimally coupled relativistic fluid and $k$-essence scalar field in a flat Friedmann-Lemaitre-Robertson-Walker universe. By adding a non-minimal coupling term in the Lagrangian level, we study the variation of Lagrangian with respect to independent variables, which produces modified scalar field and Friedmann equations. Using dynamical stability approach in different types of interaction models with two types of scalar field potential, we explore this coupled framework. Implementing detailed analysis, we can conclude our models can able to produce stable late-time cosmic acceleration.

##### 13.Starobinsky inflation and its spin-offs in the light of exact solutions

**Authors:**Jose Mathew

**Abstract:** In this paper, we discuss a general method to obtain exact cosmological solutions in modified gravity, to demonstrate the method it is employed to obtain exact cosmological solutions in $f(R,\phi)$ gravity. Here, we show that, given a particular evolution of the Universe, we could obtain different models of gravity that give that evolution, using the same construction. Further, we obtain an exact inflationary solution for Starobinsky action with a negligible cosmological constant. This analysis helps us to have a better understanding of Starobinsky inflation. With our analysis we could refine the parameter values and predictions of Starobinsky inflation. Also, we make an observation that there exist a no-go theorem for a bounce from Starobinsky action in the absence of scalar fields or a cosmological constant.

##### 14.Probing general relativistic spin-orbit coupling with gravitational waves from hierarchical triple systems

**Authors:**Marius A. Oancea, Richard Stiskalek, Miguel Zumalacárregui

**Abstract:** Wave packets propagating in inhomogeneous media experience a coupling between internal and external degrees of freedom and, as a consequence, follow spin-dependent trajectories. These are known as spin Hall effects, which are well known in optics and condensed matter physics. Similarly, the gravitational spin Hall effect is expected to affect the propagation of gravitational waves on curved spacetimes. In this general-relativistic setup, the curvature of spacetime acts as impurities in a semiconductor or inhomogeneities in an optical medium, leading to a frequency- and polarization-dependent propagation of wave packets. In this letter, we study this effect for strong-field lensed gravitational waves generated in hierarchical triple black hole systems in which a stellar-mass binary merges near a more massive black hole. We calculate how the gravitational spin Hall effect modifies the gravitational waveforms and show its potential for experimental observation. If detected, these effects will bear profound implications for astrophysics and tests of general relativity.

##### 15.Dynamical system analysis in multiscalar-torsion cosmology

**Authors:**Genly Leon
Catolica del Norte U. and DUT, Durban, Andronikos Paliathanasis
DUT, Durban and Catolica del Norte U.

**Abstract:** We explore the phase-space of a multiscalar-torsion gravitational theory within a cosmological framework characterized by a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker model. Our investigation focuses on teleparallelism and involves a gravitational model featuring two scalar fields, where one scalar field is coupled to the torsion scalar. We consider coupling in the two scalar fields' kinetic and potential components. We employ exponential functions for the scalar field potentials and analyse the field equations' stationary points to reconstruct the cosmological evolution. Remarkably, we discover many stationary points in this multiscalar field model, capable of describing various eras of cosmological evolution. Hence, this model can be used to describe the early and time acceleration phases of the universe and as a unification model for the elements of the dark sector of the universe.

##### 16.Black Holes as a Collider of High Energy Particles

**Authors:**Bobur Turimov, Shuhrat Hayitov

**Abstract:** According to the Banados-Silk-West (BSW) process, rotating black holes can act as particle colliders capable of achieving arbitrarily high center-of-mass energy (CME), provided that a specific angular momentum of one of the particles is present. In this discussion, we demonstrate that both Kerr black holes and Schwarzschild black holes could serve as potential sources of high-energy particles in the polar region.

##### 1.A full waveform model for arbitrarily axis-symmetric black hole mergers

**Authors:**Song Li, Wen-Biao Han

**Abstract:** In this work, we present a non-GR full waveform for general parametrization of axisymmetric black holes by extending our previous PSI model. Our model comprises two main components: an inspiral part obtained by using phenomenological method in frequency-domain and a ringdown part derived from quasinormal modes associated with photon motion. For quantitatively revealing the influence of the deviation from Kerr black holes on the waveforms, we specify our model to the bumpy black holes, which are typical examples of non-GR black holes. The results show that the deviation from the Kerr quadrupole moment could be measured in a high accuracy. The new waveform model can be directly used to test black holes for the LIGO-Virgo-KAGRA observations, the third generation detectors and space-borne interferometers.

##### 2.Sommerfeld law in quantum vacuum

**Authors:**G. E. Volovik

**Abstract:** The activation temperature $T$ in the de Sitter environment is twice larger than the Gibbons-Hawking temperature, related to the cosmological horizon. We consider the activation temperature as the local temperature of the de Sitter vacuum, and construct the local thermodynamics of the de Sitter state. This thermodynamics includes also the gravitational coupling $K$ and the scalar Riemann curvature ${\cal R}$ as the thermodynamically conjugate variables. These variables modify the thermodynamics of the Gibbs-Duhem relation in the de Sitter state. The free energy density is proportional to $-T^2$, which is similar to that in the non-relativistic Fermi liquids and in relativistic matter with equation of state $w=1$. The local entropy is proportional to the local temperature, while the total entropy inside the cosmological horizon is $A/4G$, where $A$ is the area of the horizon. This entropy is usually interpreted as the entropy of the cosmological horizon. We also consider the possible application of the de Sitter thermodynamics to the Schwarzschild-de Sitter black hole and to black and white holes with the de Sitter cores.

##### 3.The effects of orbital precession on hyperbolic encounters

**Authors:**Marienza Caldarola, Sachiko Kuroyanagi, Savvas Nesseris, Juan Garcia-Bellido

**Abstract:** The hyperbolic encounters of two massive objects are characterized by the emission of a gravitational wave burst, with most of the energy released during the closest approach (near the periastron). The detection of such events, different from the well-known inspiral emission, would be an interesting discovery and provide complementary information to observations of binary mergers of black holes and neutron stars in the observable Universe, shedding light, for instance, on the clustering properties of black holes and providing valuable hints on their formation scenario. Here, we analyse the dynamics of such phenomena in the simplest case where two compact objects follow unbound/hyperbolic orbits. Moreover, we explore the effects of orbital precession on the gravitational wave emission, since the precession encodes certain general relativistic effects between two bodies. We also provide templates for the strain of gravitational waves and the power spectrum for the emission, and analytical expressions for the memory effect associated with such signals.

##### 4.Hybrid Geometrodynamics: A Hamiltonian description of classical gravity coupled to quantum matter

**Authors:**J. L. Alonso, C. Bouthelier-Madre, J. Clemente-Gallardo, D. Martínez-Crespo

**Abstract:** We generelize the Hamiltonian picture of General Relativity coupled to classical matter, known as geometrodynamics, to the case where such matter is described by a Quantum Field Theory in Curved Spacetime, but gravity is still described by a classical metric tensor field over a spatial hypersurface and its associated momentum. Thus, in our approach there is no non-dynamic background structure, apart from the manifold of events, and the gravitational and quantum degrees of freedom have their dynamics inextricably coupled. Given the Hamiltonian nature of the framework, there is no need to search for a consistent quantum stress-energy tensor, but instead we work with the generators of hypersurface deformations over the manifold of quantum states. The construction relies heavily on the differential geometry of a fibration of the set of quantum states over the set of gravitational variables, and the introduction of a notion of quantum connection. The most remarkable physical implications of the construction are norm conservation of the quantum state (even if the total dynamics are non-unitary), the clear identification of the hybrid conserved quantities and the description of a dynamical backreaction of quantum matter on geometry and vice versa, which shall modify the physical properties the gravitational field would have in the absence of backreaction.

##### 5.The Schwinger effect by axial coupling in natural inflation model

**Authors:**Mehran Kamarpour

**Abstract:** We investigate the process of the Schwinger effect by axial coupling in the natural single-field inflation model in two parts. First we consider the Schwinger effect when the conformal invariance of Maxwell action should be broken by axial coupling $ I(\phi)F_{\mu\nu}\tilde{F}^{\mu\nu} $ with the inflaton field by identifying the standard horizon scale $ k=aH $ at the very beginning of inflation for additional boundary term and use several values of coupling constant $ \chi_{1} $ and estimate electric and magnetic energy densities and energy density of produced charged particles due to the Schwinger effect.We find that for both coupling functions the energy density of the produced charged particles due to the Schwinger effect is so high and spoils inflaton field.In fact the strong coupling or back-reaction occurs because the energy density of produced charged particles is exceeding of inflaton field.We use two coupling functions to break conformal invariance of maxwell action.The simplest coupling function $ I\left(\phi\right)=\chi_{1}\frac{\phi}{M_{p}} $ and a curvature based coupling function $ I\left(\phi\right)= 12\chi_{1}e^{\left(\sqrt{\frac{2}{3}}\frac{\phi}{M_{p}}\right)}\left[\frac{1}{3M_{p}^{2}}\left(4V\left(\phi\right)\right)+\frac{\sqrt{2}}{\sqrt{3}M_{p}}\left(\frac{dV}{d\phi}\right)\right] $ where $V\left(\phi\right) $ is the potential of natural inflation. In second part , in oder to avoid strong back-reaction problem we identify the horizon scale $ k_{H}=aH|\zeta| , \zeta=\frac{{I}^{\prime}\left(\phi\right)\dot{\phi}}{H} $ in which a given Fourier begins to become tachyonically unstable.The effect of this scale is reducing the value of coupling constant $ \chi_{1} $ and weakening the back-reaction problem but in both cases strong coupling or strong back-reaction exists and the Schwinger effect is impossible.

##### 6.Vacuum Zero Point Energy and its Statistical Correlations in dS Background

**Authors:**Hassan Firouzjahi, Haidar Sheikhahmadi

**Abstract:** We study the vacuum zero point energy associated to a scalar field with an arbitrary mass and conformal coupling in a dS background. Employing dimensional regularization scheme, we calculate the regularized zero point energy density, pressure and the trace of the energy momentum tensor. It is shown that the classical relation $\langle T \rangle =-4 \langle \rho \rangle$ for the vacuum stress energy tensor receives anomalous quantum correction which depends on the mass and the conformal coupling while the relation $\langle \rho \rangle = - \langle P \rangle$ does hold. We calculate the density contrast associated to the vacuum zero point energy and show that $\delta \rho \sim \langle \rho \rangle$ indicating an inhomogeneous and non-perturbative distribution of the zero point energy. Finally, we calculate the skewness associated to the distribution of the zero point energy and pressure and show that they are highly non-Gaussian.

##### 7.Effects of spin-orbit coupling on gravitational waveforms from a triaxial non-aligned neutron star in a binary system

**Authors:**Wen-Fan Feng, Tan Liu, Jie-Wen Chen, Yan Wang, Soumya D. Mohanty

**Abstract:** Spinning neutron stars (NSs) will emit continuous gravitational waves (GWs) that carry a wealth of information about the compact object. If such a signal is detected, it will provide us with new insight into the physical properties of the matter under extreme conditions. According to binary population synthesis simulations, future space-based GW detectors, such as LISA and TianQin, can potentially detect some double NSs in tight binaries with orbital periods shorter than 10 minutes. Targeted searches for continuous GWs from the spinning NS in such a binary system identified by LISA/TianQin will be possible with the proposed next-generation ground-based GW observatories, such as Cosmic Explorer and Einstein Telescope. Searching for continuous GWs from such a tight binary system requires highly accurate waveform templates that account for the interaction of the NS with its companion. In this spirit, we derive analytic approximate GWs emitted by a triaxial non-aligned NS in a binary system in which the effects of spin-orbit coupling have been incorporated. The difference with the widely used waveform for the isolated NS is estimated and the parameter estimation accuracy of the signals using Cosmic Explorer is calculated. For a typical tight double NS system with a 6~min orbital period, the angular frequency correction of the spinning NS in this binary due to spin precession is $\sim 10^{-6}~{\rm Hz}$, which is in the same order of magnitude as the angular frequency of orbital precession. The fitting factor between the waveforms with and without spin precession will drop to less than 0.97 after a few days ($\sim 10^5~{\rm s}$). We find that spin-orbit coupling has the potential to improve the accuracy of parameter estimation, especially for the binary inclination angle and spin precession cone opening angle, by up to 3 orders of magnitude.

##### 8.Detecting new fundamental fields with Pulsar Timing Arrays

**Authors:**Chao Zhang, Ning Dai, Qing Gao, Yungui Gong, Tong Jiang, Xuchen Lu

**Abstract:** Strong evidence of the existence of the Stochastic Gravitational-Wave Background (SGWB) has been reported by the NANOGrav, PPTA, EPTA and CPTA collaborations. The Bayesian posteriors of the Gravitational-Wave Background (GWB) amplitude and spectrum are compatible with current astrophysical predictions for the GWB from the population of supermassive black hole binaries (SMBHBs). In this paper, we discuss the corrections arising from the extra scalar or vector radiation to the characteristic dimensionless strain in PTA experiments and explore the possibility to detect charges surrounding massive black holes, which could give rise to SGWB with vector or scalar polarizations. The parametrized frequency-dependent characteristic dimensionless strain is used to take a Bayesian analysis and the Bayes factor is also computed for charged and neutral SMBHBs. The Bayesian posterior of GWB tensor amplitude is $\log_{10} A_T=-14.85^{+0.26}_{-0.38}$ and spectral exponent $\alpha=-0.60^{+0.32}_{-0.36}$. The Bayesian posterior for vector or scalar amplitude $A_{V, S}$ is nearly flat and there is nearly no constraint from the current observation data. The Bayesian factor is $0.71$ far less than 100, so the current observation can not support the existence of the charged SMBHB.

##### 9.Asymptotic tails of massive gravitons in light of pulsar timing array observations

**Authors:**R. A. Konoplya, A. Zhidenko

**Abstract:** We demonstrate that the asymptotic oscillatory tails of massive gravitons, present in both massive theories of gravity and effectively in extra-dimensional scenarios, could potentially contribute to gravitational waves with very long wavelengths. However, their impact on recent pulsar timing array observations is expected to be relatively small, predominantly consisting of radiation emitted by black holes in our region of the Milky Way.

##### 10.The impact of compact binary confusion noise on tests of fundamental physics with next-generation gravitational-wave detectors

**Authors:**Luca Reali, Andrea Maselli, Emanuele Berti

**Abstract:** Next-generation ground-based gravitational-wave observatories such as the Einstein Telescope and Cosmic Explorer will detect $O(10^{5}-10^{6})$ signals from compact binary coalescences every year, the exact number depending on uncertainties in the binary merger rate. Several overlapping signals will be present in band at any given time, generating a confusion noise background. We study how this confusion noise affects constraints on possible deviations from general relativity induced by modified gravity and environmental effects. Confusion noise impacts only the signals that last longer in band. Even for a "golden" GW170817-like signal, the constraints broaden by a factor in the range $[10\%,40\%]$ $([70\%,110\%])$ for the fiducial (highest) value of the local binary neutron star merger rate. Our ability to test general relativity or constrain environmental effects will be limited by systematic errors, and not by confusion noise.

##### 11.Unruh entropy of Schwarzschild black hole

**Authors:**M. Teslyk, L. Bravina, E. Zabrodin, O. Teslyk

**Abstract:** The entropy produced by the Unruh radiation is estimated and compared to the entropy of a Schwarzschild black hole. We simulate a spherical system of mass $ M $ by set of Unruh horizons and estimate the total entropy of the outgoing radiation. Dependence on mass and spin of the emitted particles is taken into account. The obtained results can be easily extended to any other intrinsic degrees of freedom of outgoing particles. The ratio of Unruh entropy to the Schwarzschild black hole entropy is derived in exact analytical form. For large black holes this ratio is highly sensitive to quantum numbers of emitted quanta, e.g., spin $ s $, for which it varies from $ 0\% $ for $ s = 0 $ to $ 19\% $ for $ s = 5/2 $.

##### 12.Gravity as embedding theory and the distribution of matter in galaxies

**Authors:**S. A. Paston, A. D. Kapustin

**Abstract:** The description of gravity in the form of an embedding theory is based on the hypothesis that our space-time is a four-dimensional surface in a flat ten-dimensional space. The choice of standard Einstein-Hilbert action leads in this case to more general field equations than Einstein's equations. By writing them in the form of Einstein's equations with the contribution of additional fictitious matter, one can try to interpret this matter as dark matter. In order to study the behavior of this fictitious matter near the centers of real galaxies, we discuss an analytical method of obtaining corresponding matter density profiles. This method is based on the consideration of the distribution function of particles over all possible trajectories and allows us to estimate the type (core or cusp) of the emerging density profile.

##### 13.Differential curvature invariants and event horizon detection for accelerating Kerr-Newman black holes in (anti-)de Sitter spacetime

**Authors:**G. V. Kraniotis

**Abstract:** We compute analytically differential invariants for accelerating, rotating and charged black holes with a cosmological constant $\Lambda$. In particular, we compute in closed form novel explicit algebraic expressions for curvature invariants constructed from covariant derivatives of the Riemann and Weyl tensors, such as the Karlhede and the Lake-Abdelqader invariants, for the Kerr-Newman-(anti-)de Sitter and accelerating Kerr-Newman-(anti-)de Sitter black hole spacetimes. We explicitly show that some of the computed curvature invariants are vanishing on the event and Cauchy horizons and/or the ergosurface of the accelerating, charged and rotating black holes with a non-zero cosmological constant. Therefore they can serve as possible detectors of the event horizon and ergosurface for such black hole metrics which belong to the most general type D solution of the Einstein-Maxwell equations with a cosmological constant.

##### 14.HPC-driven computational reproducibility

**Authors:**Yufeng Luo, Qian Zhang, Roland Haas, Zachariah B. Etienne, Gabrielle Allen

**Abstract:** Reproducibility of results is a cornerstone of the scientific method. Scientific computing encounters two challenges when aiming for this goal. Firstly, reproducibility should not depend on details of the runtime environment, such as the compiler version or computing environment, so results are verifiable by third-parties. Secondly, different versions of software code executed in the same runtime environment should produce consistent numerical results for physical quantities. In this manuscript, we test the feasibility of reproducing scientific results obtained using the IllinoisGRMHD code that is part of an open-source community software for simulation in relativistic astrophysics, the Einstein Toolkit. We verify that numerical results of simulating a single isolated neutron star with IllinoisGRMHD can be reproduced, and compare them to results reported by the code authors in 2015. We use two different supercomputers: Expanse at SDSC, and Stampede2 at TACC. By compiling the source code archived along with the paper on both Expanse and Stampede2, we find that IllinoisGRMHD reproduces results published in its announcement paper up to errors comparable to round-off level changes in initial data parameters. We also verify that a current version of IlliinoisGRMHD reproduces these results once we account for bug fixes which has occurred since the original publication

##### 15.Towards exponentially-convergent simulations of extreme-mass-ratio inspirals: A time-domain solver for the scalar Teukolsky equation with singular source terms

**Authors:**Manas Vishal, Scott E. Field, Katherine Rink, Sigal Gottlieb, Gaurav Khanna

**Abstract:** Gravitational wave signals from extreme mass ratio inspirals are a key target for space-based gravitational wave detectors. These systems are typically modeled as a distributionally-forced Teukolsky equation, where the smaller black hole is treated as a Dirac delta distribution. Time-domain solvers often use regularization approaches that approximate the Dirac distribution that often introduce small length scales and are a source of systematic error, especially near the smaller black hole. We describe a multi-domain discontinuous Galerkin method for solving the distributionally-forced Teukolsky equation that describes scalar fields evolving on a Kerr spacetime. To handle the Dirac delta, we expand the solution in spherical harmonics and recast the sourced Teukolsky equation as a first-order, one-dimensional symmetric hyperbolic system. This allows us to derive the method's numerical flux to correctly account for the Dirac delta. As a result, our method achieves global spectral accuracy even at the source's location. To connect the near field to future null infinity, we use the hyperboloidal layer method, allowing us to supply outer boundary conditions and providing direct access to the far-field waveform. We document several numerical experiments where we test our method, including convergence tests against exact solutions, energy luminosities for circular orbits, the scheme's superconvergence properties at future null infinity, and the late-time tail behavior of the scalar field. We also compare two systems that arise from different choices of the first-order reduction variables, finding that certain choices are numerically problematic in practice. The methods developed here may be beneficial when computing gravitational self-force effects, where the regularization procedure has been developed for the spherical harmonic modes and high accuracy is needed at the Dirac delta's location.

##### 1.Separating the superradiant emission from the Hawking radiation from a rotating black hole

**Authors:**De-Chang Dai, Dejan Stojkovic

**Abstract:** Emission of particles created in the background of a rotating black hole can be greatly amplified taking away rotational energy of a black hole. This amplification affects both particles created near the horizon (due to the Hawing effect), and particles created near the potential barrier far from the horizon. Only the latter effect is called the superradiance in the strict sense. We explicitly calculate the superradiant emission for scalar particles and compare it with the total scalar particle emission (Hawking radiation plus superradiance) to clarify some confusion in the literature. We clearly show that these two emissions are not the same. In particular, superradiance persists even for extremal black holes whose Hawking temperature is zero.

##### 2.Is it possible to measure the Lense-Thirring orbital shifts of the short-period S-star S4716 orbiting Sgr A$^\ast$?

**Authors:**Lorenzo Iorio

**Abstract:** The maximal values of the general relativistic Lense-Thirring (LT) orbital shifts $\Delta I^\mathrm{LT},\,\Delta\Omega^\mathrm{LT}$ and $\Delta\omega^\mathrm{LT}$ of the inclination $I$, the longitude of the ascending node $\Omega$ and the perinigricon $\omega$ of the recently discovered star S4716, which has the shortest orbital period $\left(P_\mathrm{b}=4.02\,\mathrm{yr}\right)$ of all the S-stars that orbit the supermassive black hole (SMBH) in Sgr A$^\ast$, are of the order of $\simeq 5-16$ arcseconds per revolution $\left(^{\prime\prime}\,\mathrm{rev}^{-1}\right)$. Given the current error $\sigma_\omega = 0.02^\circ$ in determining $\omega$, which is the most accurate orbital parameter of S4716 among all those affected by the SMBH's gravitomagnetic field through its angular momentum ${\boldsymbol{J}}_\bullet$, about 48 yr would be needed to reduce $\sigma_\omega$ to $\simeq 10\%$ of the cumulative LT perinigricon shift over the same time span. Measuring $\Delta I^\mathrm{LT}$ and $\Delta\Omega^\mathrm{LT}$ to the same level of accuracy would take even much longer. Instead, after just 16 yr, a per cent measurement of the larger gravitoelectric (GE) Schwarzschild-like perinigricon shift $\Delta\omega^\mathrm{GE}$, which depends only on the SMBH's mass $M_\bullet$, would be possible. On the other hand, the uncertainties in the physical and orbital parameters entering $\Delta\omega^\mathrm{GE}$ would cause a huge systematic bias of $\Delta\omega^\mathrm{LT}$ itself. The SMBH's quadrupole mass moment $Q_2^\bullet$ induces orbital shifts as little as $\simeq 0.01-0.05\,^{\prime\prime}\,\mathrm{rev}^{-1}$.

##### 3.Thin-Shell Gravastar Model in $f(Q,T)$ Gravity

**Authors:**Sneha Pradhan, Debasmita Mohanty, P. K. Sahoo

**Abstract:** In the last few decades, gravastars have been proposed as an alternative to black holes. The stability of the gravastar has been studied in many modified theories of gravity along with Einstein's GR. The $f(Q,T)$ gravity, a successfully modified theory of gravity for describing the current accelerated expansion of the Universe, has been used in this article to study gravastar in different aspects. According to Mazur and Mottola (Proc. Natl. Acad. Sci 101, 9545 (2004)), it has three regions with three different equations of state. Here in this work, we have studied the interior of the gravastar by considering the $p=-\rho$ EoS to describe the dark sector for the interior region. The next region is a thin shell of ultrarelativistic stiff fluid, in which we have investigated several physical properties, viz., the proper length, energy, entropy, surface energy density, etc. In addition, we have studied the surface redshift and speed of sound to check the potential stability of our proposed thin-shell gravastar model. Apart from that, we have used the entropy maximization technique to verify the stability of the gravastar model. The gravastar's outer region is a complete vacuum described by exterior Schwarzschild geometry. Finally, we have presented a stable gravastar model which is singularity-free and devoid of any incompleteness in classical black hole theory.

##### 4.Total light deflection in the gravitational field of an axisymmetric body at rest with full mass and spin multipole structure

**Authors:**Sven Zschocke

**Abstract:** The tangent vector of the light trajectory at future infinity and the angle of total light deflection in the gravitational field of an isolated axisymmetric body at rest with full set of mass-multipoles and spin-multipoles is determined in harmonic coordinates in the 1PN and 1.5PN approximation of the post-Newtonian (PN) scheme. It is found that the evaluation of the tangent vector and of the angle of total light deflection caused by mass-multipoles and spin-multipoles leads directly and in a compelling way to Chebyshev polynomials of first and second kind, respectively. This fact allows to determine the upper limits of the total light deflection, which are strictly valid in the 1PN and 1.5PN approximation. They represent a criterion to identify those multipoles which contribute significantly to the total light deflection for a given astrometric accuracy. These upper limits are used to determine the total light deflection in the gravitational field of the Sun and giant planets of the solar system. It is found that the first few mass-multipoles with l \le 10 and the first few spin-multipoles with l \le 3 are sufficient for an accuracy on the nano-arcsecond level in astrometric angular measurements.

##### 5.On the possibility of classical vacuum polarization and magnetization

**Authors:**Sébastien Fumeron, Fernando Moraes, Bertrand Berche

**Abstract:** It is common practice to take for granted the equality (up to the constant $\varepsilon_0$) of the electric displacement ($\bf{D}$) and electric ($\bf{E}$) field vectors in vacuum. The same happens with the magnetic field ($\bf{H}$) and the magnetic flux density ($\bf{B}$) vectors (up to the constant $\mu_0^{-1}$). The fact that gravity may change this by effectively inducing dielectric or magnetic responses to the primary fields is commonly overlooked. It is the purpose of this communication to call attention to classical polarization or magnetization of the vacuum due to the concomitant presence of gravitational and electromagnetic sources. The formalism of differential forms (exterior calculus) is used since it provides a clear-cut way to achieve this. This work offers new routes for possible detection of various spacetime geometries via their electromagnetic manifestations and the way they influence light propagation.

##### 6.On the resilience of the gravitational boundary value problem under renormalization

**Authors:**Giulio Neri, Stefano Liberati

**Abstract:** A well-defined variational principle for gravitational actions typically requires to cancel boundary terms produced by the variation of the bulk action with a suitable set of boundary counterterms. This can be achieved by carefully balancing the coefficients multiplying the bulk operators with those multiplying the boundary ones. A typical example of this construction is the Gibbons-Hawking-York boundary action that needs to be added to the Einstein-Hilbert one in order to have a well-defined metric variation for General Relativity with Dirichlet boundary conditions. Quantum fluctuations of matter fields lead to the renormalization of said coefficients which may or may not preserve this balance. Indeed, already at the level of General Relativity, the resilience of the matching between bulk and boundary constants is far from obvious and it is anyway incomplete given that matter generically induces quadratic curvature operators. We investigate here the resilience of the matching of higher-order couplings upon renormalization by a non-minimally coupled scalar field and show that a problem is present. Even though we do not completely solve the latter, we show that it can be greatly ameliorated by a wise splitting between dynamical and topological contributions. Doing so, we find that the bulk-boundary matching is preserved up to a universal term whose nature and possible cancellation we shall discuss in the end.

##### 7.Intrinsic rigidity of extremal horizons

**Authors:**Maciej Dunajski, James Lucietti

**Abstract:** We prove that the intrinsic geometry of compact cross-sections of any vacuum extremal horizon must admit a Killing vector field. If the cross-sections are two-dimensional spheres, this implies that the most general solution is the extremal Kerr horizon and completes the classification of the associated near-horizon geometries. The same results hold with a cosmological constant. Furthermore, we also deduce that any non-trivial vacuum near-horizon geometry, with a non-positive cosmological constant, must have an SO(2,1) isometry in all dimensions under no symmetry assumptions. We also show that, if the cross-sections are two-dimensional, the horizon Einstein equation is equivalent to a single fourth order PDE for the K\"ahler potential, and that this equation is explicitly solvable on the sphere if the corresponding metric admits a Killing vector.

##### 8.Nonlinear Yang-Mills black holes

**Authors:**Fatemeh Masoumi Jahromi, Behrouz Mirza, Fatemeh Naeimipour, Soudabe Nasirimoghadam

**Abstract:** This paper is devoted to investigating the nonlinear non-abelian Yang-Mills black holes. We consider three Born-Infeld, exponential, and logarithmic nonlinear Yang-Mills theories with $SO(n-1)$ and $SO(n-2,1)$ semi-simple groups, which n is the dimension of spacetime, and obtain a new class of nonlinear Yang-Mills (NYM) black hole solutions. Depending on the values of dimension $n$, Yang-Mills charge $e$ and the mass $m$ and nonlinear parameters $\beta$, our solutions can lead to a naked singularity, a black hole with two horizons, an extreme or a Schwarzschild-type black hole. We also investigate the thermodynamic behaviors of the NYM black holes. For small charge values, the NYM solutions may be thermally stable in the canonical ensemble, if we consider an AdS spacetime with spherical $k=+1$ and hyperbolic $k=-1$ coordinates or a flat one with $k=+1$. However, there are no stable regions in the grand canonical ensemble in higher dimensions. For the NYM black hole, we observe a reentrant phase transition between large and small black holes in the BI-branch with small $\beta$, which cannot be visible for the nonlinear Reissner-Nordstrom AdS black hole in the higher dimension. For the limit $\beta\rightarrow\infty$, the critical ratio $\frac{P_{c} v_{c}}{T_{c}}$ tends to the constant value $3/8$ for each dimension $n$, while it depends on the dimension for the case of nonlinear electrodynamics black holes.

##### 9.Supermassive primordial black holes in multiverse: for nano-Hertz gravitational wave and high-redshift JWST galaxies

**Authors:**Hai-Long Huang, Yong Cai, Jun-Qian Jiang, Jun Zhang, Yun-Song Piao

**Abstract:** Recently, observational hints for supermassive black holes have been accumulating, which has inspired ones to wonder: Can primordial black holes (PBHs) be supermassive, in particular with the mass $M\gtrsim 10^{9}M_\odot$? A supercritical bubble (with an inflating baby universe inside it) that nucleated during inflation can develop into a PBH in our observable Universe. Here, we find that when the inflaton slowly passes by a neighboring vacuum, the nucleating rate of supercritical bubbles would inevitably attain a peak, so the mass distribution of multiverse PBHs, and the mass of peak can be up to $M\gtrsim 10^{11}M_\odot$. Thus our mechanism naturally provides a primordial origin of supermassive BHs.

##### 10.Extracting electromagnetic signatures of spacetime fluctuations

**Authors:**B. Sharmila, Sander M. Vermeulen, Animesh Datta

**Abstract:** We present a formalism to discern the effects of fluctuations of the spacetime metric on electromagnetic radiation. The formalism works via the measurement of electromagnetic field correlations, while allowing a clear assessment of the assumptions involved. As an application of the formalism, we present a model of spacetime fluctuations that appear as random fluctuations of the refractive index of the vacuum in single, and two co-located Michelson interferometers. We compare an interferometric signal predicted using this model to experimental data from the Holometer and aLIGO. We show that if the signal manifests at a frequency at which the interferometers are sensitive, the strength and scale of possible spacetime fluctuations can be constrained. The formalism enables us to evaluate proposed experiments such as QUEST for constraining quantum spacetime fluctuations and to even potentially formulate new experiments.

##### 11.From quantum gravity to gravitational waves through cosmic strings

**Authors:**Astrid Eichhorn, Rafael R. Lino dos Santos, João Lucas Miqueleto

**Abstract:** New physics beyond the Standard Model can give rise to stochastic gravitational wave backgrounds, for example through cosmic strings. In this way, gravitational-wave searches with pulsar-timing arrays as well as existing and future laser interferometers may provide information on particle physics beyond the Standard Model. Here, we take one additional step and link particle physics beyond the Standard Model to quantum gravity. We investigate whether particle physics models that may give rise to cosmic strings can be embedded into an asymptotically safe theory of quantum gravity and matter. We focus on models where cosmic strings arise from U(1)-symmetry-breaking in an extended Yukawa-Abelian-Higgs sector that may be part of a dark sector. We find a negative answer for the simplest model that can give rise to cosmic strings and also find constraints on an extended model. We tentatively conclude that cosmic strings are difficult to accommodate in asymptotically safe models. This fits well with the latest 15-year dataset and search for new physics from the NANOGrav collaboration, which disfavors a stable-cosmic-string interpretation. In that sense, the recent data provide an indirect, albeit at present rather tentative, hint about the quantum theory of gravity.

##### 12.Imprints of primordial gravitational waves with non-Bunch-Davies initial states on CMB bispectra

**Authors:**Shingo Akama, Hiroaki W. H. Tahara

**Abstract:** It has been shown that both scalar and tensor modes with non-Bunch-Davies initial states can enhance the amplitudes of the primordial bispectra compared to those with the Bunch-Davies state, especially for wavenumber modes in a flattened triangle configuration. However, in the case of the non-Bunch-Davies scalar modes, it has also been found that those enhancements in Fourier space are somewhat reduced in bispectra of cosmic microwave background (CMB) fluctuations. In this paper, we show that the enhancement resulting from the tensor modes is partially reduced to a degree differing from that of the scalar modes, which makes the non-Bunch-Davies effects unobservable in gravitational theories with the same quadratic and cubic operators of the tensor perturbations as general relativity. Furthermore, we present examples of gravitational theories yielding enhancements that would potentially be detected through CMB experiments.

##### 13.Enhanced plateau effect at resonance in realistic non-integrable EMRIs

**Authors:**Areti Eleni, Theocharis A. Apostolatos

**Abstract:** When an EMRI in a perturbed integrable gravitational field, such as a deformed Kerr black hole, undergoes a prolonged resonance, the frequencies that engage in resonance retain a fixed rational ratio, despite experiencing adiabatic changes due to radiation reaction. In the past this plateau effect in the evolution of the ratio of frequencies has been investigated by studying the orbital evolution through kludge models, which provide approximate average losses of energy and angular momentum experienced by a test particle in this field. By employing a Newtonian gravitational field that closely resembles a pure Kerr or a perturbed Kerr relativistic field, we demonstrate that the actual adiabatic evolution of an orbit driven by an artificial ``self-force'' results in more prolonged periods of resonance crossings compared to those obtained by imposing a predetermined rate of energy and angular momentum change throughout the orbital progression.

##### 14.Future stability of expanding spatially homogeneous FLRW solutions of the spherically symmetric Einstein--massless Vlasov system with spatial topology $\mathbb{R}^3$

**Authors:**Martin Taylor

**Abstract:** Spatially homogeneous FLRW solutions constitute an infinite dimensional family of explicit solutions of the Einstein--massless Vlasov system with vanishing cosmological constant. Each member expands towards the future at a decelerated rate. These solutions are shown to be nonlinearly future stable to compactly supported spherically symmetric perturbations, in the case that the spatial topology is that of $\mathbb{R}^3$. The decay rates of the energy momentum tensor components, with respect to an appropriately normalised double null frame, are compared to those around Minkowski space. When measured with respect to their respective $t$ coordinates, certain components decay faster around Minkowski space, while others decay faster around FLRW.

##### 15.Entropy Product Function and Central charges in NUT Geometry

**Authors:**Parthapratim Pradhan

**Abstract:** We define an \emph{entropy product function}~(EPF) for Taub-Newman-Unti-Tamburino~(TNUT) black hole~(BH) following the prescription suggested by Wu et al.~\cite{wu} ~[PRD 100, 101501(R) (2019)]. The prescription argues that a generic four-dimensional TNUT spacetime might be expressed in terms of three or four different types of thermodynamic hairs. They can be defined as the Komar mass~($M=m$), the angular momentum~($J_{n}=mn$), the gravitomagnetic charge ($N=n$), the dual~(magnetic) mass $(\tilde{M}=n)$. Taking this prescription and using the \emph{EPF}, we derive the \emph{central charges} of dual CFT~(conformal field theory) via Cardy's formula. Remarkably, we \emph{find} that for TNUT BH there exists a relation between the \emph{central charges and EPF} as $c=6\left(\frac{\partial {\cal F}}{\partial {\cal N}_{i}}\right)$, where ${\cal F}$ is EPF and ${\cal N}_{i}$ is one of the integer-valued charges i.e. the NUT charges~($N$) or any new conserved charges~($J_{N}$). We reverify these results by calculating the exact values of different thermodynamic parameters. We define the EPF~${\cal F}$ from the first law of thermodynamics of both horizons. Moreover, we write the first laws of both the horizons for left-moving and right-moving sectors. Introducing the B\'{e}zout's identity, we show that for TNUT BH one can generate more holographic descriptions described by a pair of integers $(a,b)$. More holographic pictures have a great significance in understanding the holographic nature of quantum gravity. Furthermore, using the \emph{EPF} we derive the central charges for Reissner-Nordstr\"{o}m-NUT~(RNNUT) BH, Kerr-Taub-NUT~(KNUT) BH and Kerr-Newman-NUT~(KNNUT) BH. Finally, we prove that they are equal in both sectors provided that the EPF is mass-independent~(or universal).

##### 16.Limits on scalar-induced gravitational waves from the stochastic background by pulsar timing array observations

**Authors:**Yi-Fu Cai, Xin-Chen He, Xiaohan Ma, Sheng-Feng Yan, Guan-Wen Yuan

**Abstract:** Recently, the NANOGrav, PPTA, EPTA and CPTA collaborations independently reported their evidence of the Stochastic Gravitational Wave Background (SGWB). While the inferred gravitational-wave background amplitude and spectrum are consistent with astrophysical expectations for a signal from the population of supermassive black-hole binaries (SMBHB), the search for new physics remains plausible in this observational window. In this work, we explore the possibility of explaining such a signal by the scalar-induced gravitational waves (IGWs) in the very early universe. We use a parameterized broken power-law function as a general description of the energy spectrum of the SGWB, and fit it to the newly released results of NANOGrav and PPTA. We find that this method can lead to tight limits on the parameter space of IGWs and further yield restrictions on various inflation models that may produce PBHs in the early universe, which is also expected to be examined by the forthcoming space-based GW experiments.

##### 17.Wormholes with matter haunted by conformally coupled ghosts

**Authors:**Bruno J. Barros, Álvaro de la Cruz-Dombriz, Francisco S. N. Lobo

**Abstract:** In this work, we present novel analytical solutions for static and spherically symmetric wormhole geometries threaded by an anisotropic distribution of matter conformally coupled to a scalar ghost field. We explore the main features of the theory, such as the dynamics of the scalar field and matter throughout the wormhole, as well as the role played by the non-minimal coupling. Furthermore, coupled ghosts in the presence of a scalar potential are considered and traversability conditions are analysed within such geometrical scheme. More specifically, we find analytical solutions that although the energy density of the ghost is strictly negative, the energy density of matter may attain positive values.

##### 18.Domain wall interpretation of the PTA signal confronting black hole overproduction

**Authors:**Yann Gouttenoire, Edoardo Vitagliano

**Abstract:** Recently, NANOGrav has reported the observation of a stochastic gravitational wave background (SGWB) at nano-Hertz frequencies. String-wall networks and domain walls have been proposed as possible sources. To be cosmologically viable, these topological defect networks must annihilate before they dominate the energy budget of the universe, producing a SGWB. However, a part of the network can copiously produce primordial black holes that exceed current bounds. Performing a Bayesian analysis of pulsar timing residual datasets we find that the SGWB detected in PTA data is therefore hardly compatible with such an origin. This lends credibility to other interpretations, including supermassive black hole mergers, first order phase transitions, Nambu-Goto strings, and curvature-induced gravitational waves.

##### 19.Second-order perturbations of the Schwarzschild spacetime: practical, covariant and gauge-invariant formalisms

**Authors:**Andrew Spiers, Adam Pound, Barry Wardell

**Abstract:** High-accuracy gravitational-wave modeling demands going beyond linear, first-order perturbation theory. Particularly motivated by the need for second-order perturbative models of extreme-mass-ratio inspirals and black hole ringdowns, we present practical spherical-harmonic decompositions of the Einstein equation, Regge-Wheeler-Zerilli equations, and Teukolsky equation at second perturbative order in a Schwarzschild background. Our formulations are covariant on the $t$--$r$ plane and on the two-sphere, and we express the field equations in terms of gauge-invariant metric perturbations. In a companion \pkg{Mathematica} package, \pkg{PerturbationEquations}, we provide these invariant formulas as well as the analogous formulas in terms of raw, gauge-dependent metric perturbations. Our decomposition of the second-order Einstein equation, when specialized to the Lorenz gauge, was a key ingredient in recent second-order self-force calculations~[Phys. Rev. Lett. 124, 021101 (2020); ibid. 127, 151102 (2021); ibid. 130, 241402 (2023)].

##### 20.Self-interacting dipolar boson stars and their dynamics

**Authors:**Pedro Ildefonso, Miguel Zilhão, Carlos Herdeiro, Eugen Radu, Nuno M. Santos

**Abstract:** We construct and dynamically evolve dipolar, self-interacting scalar boson stars in a model with sextic (+ quartic) self-interactions. The domain of existence of such dipolar $Q$-stars has a similar structure to that of the fundamental monopolar stars of the same model. For the latter it is structured in a Newtonian plus a relativistic branch, wherein perturbatively stable solutions exist, connected by a middle unstable branch. Our evolutions support similar dynamical properties of the dipolar $Q$-stars that: 1) in the Newtonian and relativistic branches are dynamically robust over time scales longer than those for which dipolar stars without self-interactions are seen to decay; 2) in the middle branch migrate to either the Newtonian or the relativistic branch; 3) beyond the relativistic branch decay to black holes. Overall, these results strengthen the observation, seen in other contexts, that self-interactions can mitigate dynamical instabilities of scalar boson star models.

##### 21.The chaotic behavior of the Bianchi IX model under the influence of quantum effects

**Authors:**Martin Bojowald, David Brizuela, Paula Calizaya Cabrera, Sara F. Uria

**Abstract:** A quantum analysis of the vacuum Bianchi IX model is performed, focusing in particular on the chaotic nature of the system. The framework constructed here is general enough for the results to apply in the context of any theory of quantum gravity, since it includes only minimal approximations that make it possible to encode the information of all quantum degrees of freedom in the fluctuations of the usual anisotropy parameters. These fluctuations are described as canonical variables that extend the classical phase space. In this way, standard methods for dynamical systems can be applied to study the chaos of the model. Two specific methods are applied that are suitable for time-reparameterization invariant systems. First, a generalized version of the Misner-Chitre variables is constructed, which provides an isomorphism between the quantum Bianchi IX dynamics and the geodesic flow on a suitable Riemannian manifold, extending, in this way, the usual billiard picture. Secondly, the fractal dimension of the boundary between points with different outcomes in the space of initial data is numerically analyzed. While the quantum system remains chaotic, the main conclusion is that its strength is considerably diminished by quantum effects as compared to its classical counterpart.

##### 1.Gravitational synchrotron radiation and Penrose process in STVG theory

**Authors:**Bobur Turimov, Husan Alibekov, Pulat Tadjimuratov, Ahmadjon Abdujabbarov

**Abstract:** The paper has explored analogue of gravitational synchrotron massive particle and Penrose process in MOdified Gravity (MOG) known as Scalar-Tensor-Vector-Gravity (STVG). Investigation of the gravitational field around Kerr-MOG black hole showed that it has strong gravitational field with large horizon and can rotate faster than Kerr black hole due to the effect of STVG. We have studied influence of STVG in circular motion of massive particle around Kerr-MOG black hole and discussed the Innermost Stable Circular Orbit (ISCO) of massive test particle. It is shown that STVG plays a crucial role in energy extraction from a rotating black hole, with an energy efficiency of more than $100\%$ according to the Penrose process. Furthermore, we have explored the gravitational synchrotron radiation analogue produced by a massive particle orbiting around a Kerr-MOG black hole. It has been shown that the intensity of gravitational radiation from binary systems of stellar black holes (SBH) and supermassive black holes (SMBH).

##### 2.Holographic description of $F(R)$ gravity coupled with Axion Dark Matter

**Authors:**Simone D'Onofrio

**Abstract:** In this work we study the autonomous dynamical system of different $F(R)$ models in the formalism of holographic dark energy using the generalized Nojiri-Odintsov cut-off. We explicitly give the expression of the fixed points as functions of the infrared cut-off for vacuum $F(R)$ gravity in flat and non-flat FRW background and for $F(R)$ coupling axion dark matter. Each fixed point component can be taken as a condition on the cut-off and on the expression of $F(R)$, leading to physically interesting constraints on these functions.

##### 3.Note About Canonical Formalism for Gravity with Dynamical Determinant of Metric

**Authors:**J. Kluson

**Abstract:** In this short note we perform canonical analysis of the theory invariant under restricted diffeomorphism so that the action contains kinetic term for determinant of metric. We find corresponding Hamiltonian and determine structure of constraints.

##### 4.Raychaudhuri Equation from Lagrangian and Hamiltonian formulation : A Quantum Aspect

**Authors:**Madhukrishna Chakraborty, Subenoy Chakraborty

**Abstract:** The paper deals with a suitable transformation related to the metric scalar of the hyper-surface so that the Raychaudhuri Equation (RE) can be written as a second order nonlinear differential equation. A first integral of this second order differential equation gives a possible analytic solution of the RE. Also, it is shown that construction of a Lagrangian (and hence a Hamiltonian) is possible, from which the RE can be derived. Wheeler-Dewitt equation has been formulated in canonical quantization scheme and norm of it's solution (wave function of the universe) is shown to affect the singularity analysis in the quantum regime for any spatially homogeneous and isotropic cosmology. Finally Bohmian trajectories are formulated with causal interpretation and these quantum trajectories unlike classical geodesics obliterate the initial big-bang singularity when the quantum potential is included.

##### 5.The Hawking effect in the particles-partners correlations

**Authors:**Roberto Balbinot, Alessandro Fabbri

**Abstract:** We analyze the correlations functions across the horizon in Hawking black hole radiation to reveal the correlations between Hawking particles and their partners. The effect of the underlying space-time on this are shown in various examples ranging from acoustic black holes to regular black holes.

##### 6.Neutron stars in Gauss-Bonnet gravity -- nonlinear scalarization and gravitational phase transitions

**Authors:**Daniela D. Doneva, Christian J. Krüger, Kalin V. Staykov, Petar Y. Yordanov

**Abstract:** It was recently discovered that scalarized neutron stars in scalar-tensor theories can undergo a gravitational phase transition to a non-scalarized (GR) state. Surprisingly, even though the driving mechanism is totally different, the process resembles closely the first-order matter phase transition from confined nuclear matter to deconfined quark matter in neutron star cores. The studies until now were limited, though, to only one theory of gravity and a limited range of parameters. With the present paper, we aim at demonstrating that gravitational phase transitions are more common than expected. More specifically, we show that the phenomenon of nonlinear scalarization is present for neutron stars in Gauss-Bonnet gravity leading to the possibility of gravitational phase transition. Moreover, it can be observed for a wide range of parameters so no fine-tuning is needed. This solidifies the conjecture that gravitational phase transitions are an important phenomenon for compact objects and their astrophysical implications deserve an in-depth study.

##### 7.A note on null distance and causality encoding

**Authors:**Gregory J. Galloway

**Abstract:** Under natural conditions, the null distance introduced by Sormani and Vega [10] is a metric space distance function on spacetime, which, in a certain precise sense, can encode the causality of spacetime. The null distance function requires the choice of a time function. The purpose of this note is to observe that the causality assumptions related to such a choice in results used to establish global encoding of causality, due to Sakovich and Sormani [9] and to Burtscher and Garc\'ia-Heveling [2], can be weakened.

##### 8.Searching for gravitational wave burst in PTA data with piecewise linear functions

**Authors:**Heling Deng, Bence Bécsy, Xavier Siemens, Neil J. Cornish, Dustin R. Madison

**Abstract:** Transient gravitational waves (aka gravitational wave bursts) within the nanohertz frequency band could be generated by a variety of astrophysical phenomena such as the encounter of supermassive black holes, the kinks or cusps in cosmic strings, or other as-yet-unknown physical processes. Radio-pulses emitted from millisecond pulsars could be perturbed by passing gravitational waves, hence the correlation of the perturbations in a pulsar timing array can be used to detect and characterize burst signals with a duration of $\mathcal{O}(1\text{-}10)$ years. We propose a fully Bayesian framework for the analysis of the pulsar timing array data, where the burst waveform is generically modeled by piecewise straight lines, and the waveform parameters in the likelihood can be integrated out analytically. As a result, with merely three parameters (in addition to those describing the pulsars' intrinsic and background noise), one is able to efficiently search for the existence and the sky location of {a burst signal}. If a signal is present, the posterior of the waveform can be found without further Bayesian inference. We demonstrate this model by analyzing simulated data sets containing a stochastic gravitational wave background {and a burst signal generated by the parabolic encounter of two supermassive black holes.

##### 1.The Joule--Thomson and Joule--Thomson-like effects of the black holes in a cavity

**Authors:**Nan Li, Jin-Yu Li, Bing-Yu Su

**Abstract:** When a black hole is enclosed in a cavity in asymptotically flat space, an effective volume can be introduced, and an effective pressure can be further defined as its conjugate variable. By this means, an extended phase space is constructed in a cavity, which resembles that in the anti-de Sitter (AdS) space in many aspects. However, there are still some notable dissimilarities simultaneously. In this work, the Joule--Thomson (JT) effect of the black holes, widely discussed in the AdS space as an isenthalpic (constant-mass) process, is shown to only have cooling region in a cavity. On the contrary, in a constant-thermal-energy process (the JT-like effect), there is only heating region in a cavity. Altogether, different from the AdS case, there is no inversion temperature or inversion curve in a cavity. Our work reveals the subtle discrepancy between the two different extended phase spaces that is sensitive to the specific boundary conditions.

##### 2.Plane fronted electromagnetic waves and an asymptotic limit of Liénard--Wiechert fields

**Authors:**Peter A. Hogan, Dirk Puetzfeld

**Abstract:** Colliding or noncolliding plane fronted electromagnetic or gravitational waves are the asymptotic limit of Robinson--Trautman spherical electromagnetic or gravitational waves. Noncolliding plane fronted waves contain no information about their sources whereas colliding waves contain information about possibly the motion of their sources. As a first step to investigate the latter phenomenon we construct an asymptotic limit of Li\'enard--Wiechert electromagnetic fields in the context of Minkowskian space--time. This has the advantage that the source is well known and the calculations can be carried out in full detail. The final result is an algebraically general Maxwell field which consists of colliding plane fronted waves in a subregion of Minkowskian space--time and an interesting byproduct is a novel perspective on a Maxwell field originally discovered by Bateman.

##### 3.Bulk-boundary and RPS Thermodynamics from Topology perspective

**Authors:**Jafar Sadeghi, Mohammad Reza Alipour, Saeed Noori Gashti, Mohammad Ali S. Afshar

**Abstract:** In this article, we investigate the bulk-boundary and restricted phase space (RPS) thermodynamics of Rissner-Nordstr\"om (R-N) AdS and 6-dimensional charged Gauss-Bonnet AdS black holes. Also, we examine the topological characteristics of the considered black holes and compare them with the extended thermodynamics results. In fact, we have found that the topological behavior of the bulk-boundary thermodynamics is the same as that of the extended thermodynamics, whereas the RPS thermodynamics exhibits a distinct behavior. We also demonstrate that within the RPS formalism, there is only one critical point with a topological charge of +1 $(Q_t=+1)$. Additionally, for RPS formalism, the inclusion of higher derivative curvature terms in the form of Gauss-Bonnet gravity does not alter the topological classification of critical points in charged AdS black holes.

##### 4.Amplifying quantum discord during inflationary magnetogenesis through violation of parity

**Authors:**Sagarika Tripathy, Rathul Nath Raveendran, Krishnamohan Parattu, L. Sriramkumar

**Abstract:** It is well known that, during inflation, the conformal invariance of the electromagnetic action has to be broken in order to produce magnetic fields of observed strengths today. Often, to further enhance the strengths of the magnetic fields, parity is also assumed to be violated when the fields are being generated. In this work, we examine the evolution of the quantum state of the Fourier modes of the non-conformally coupled and parity violating electromagnetic field during inflation. We utilize tools such as the Wigner ellipse, squeezing parameters and quantum discord to understand the evolution of the field. We show that the violation of parity leads to an enhancement of the squeezing amplitude and the quantum discord (or, equivalently, in this context, the entanglement entropy) associated with a pair of opposite wave vectors for one of the two states of polarization (and a suppression for the other state of polarization), when compared to the case wherein parity is conserved. We highlight the similarities between the evolution of the Fourier modes of the electromagnetic field when parity is violated during inflation and the behavior of the modes of a charged, quantum, scalar field in the presence of a constant electric field in a de Sitter universe. We briefly discuss the implications of the results we obtain.

##### 5.Geometric phase in Taub-NUT spacetime

**Authors:**Chandrachur Chakraborty
MCNS-MAHE, Banibrata Mukhopadhyay
IISc

**Abstract:** Constructing the Hamiltonian in the $\eta$-representation, we explore the geometric phase in the Taub-NUT spacetime, which is spherically symmetric and stationary. The geometric phase around a non-rotating Taub-NUT spacetime reveals both the gravitational analog of Aharonov-Bohm effect and Pancharatnam-Berry phase, similar to the rotating Kerr background. On the other hand, only the latter emerges in the spherically symmetric Schwarzschild geometry as well as in the axisymmetric magnetized Schwarzschild geometry. With this result, we argue that the Aharonov-Bohm effect and Pancharatnam-Berry phase both can emerge in the stationary spacetime, whereas only the latter emerges in the static spacetime. We outline plausible measurements of these effects/phases, mostly for primordial black holes.

##### 6.The invisible low-frequency gravitons and the audio band

**Authors:**Massimo Giovannini

**Abstract:** The low-frequency gravitons correspond to typical wavelengths that left the Hubble radius during the early inflationary stages of expansion and reentered after matter radiation equality. Consequently the temperature and the polarization anisotropies of the cosmic microwave background constrain the tensor-to-scalar-ratio in the aHz region but since the audio band and the MHz domain are sensitive to the post-inflationary expansion rate, the low-frequency determinations of the tensor-to-scalar-ratio can be combined with the high-frequency constraints. In this framework we examine the possibility that the low-frequency gravitons remain invisible in the aHz region but are still potentially detectable at much higher frequencies. Because the number of $e$-folds associated with the exit of the cosmic microwave background wavelengths depends both on the slow-roll parameters and on the total expansion rate after inflation, this approach leads to a set of lower bounds on the tensor-to-scalar-ratio.

##### 1.Holographic realization from inflation to reheating in generalized entropic cosmology

**Authors:**Sergei D. Odintsov, Simone D'Onofrio, Tanmoy Paul

**Abstract:** The growing cosmological interest of different entropy functions (like the Tsallis entropy, the R\'{e}nyi entropy, the Barrow entropy, the Sharma-Mittal entropy, the Kaniadakis entropy and the Loop Quantum gravity entropy) naturally raises an important question: "Does there exist a generalized entropy that can bring all the known entropies proposed so far within a single umbrella?" In spirit of this, recently a four parameter generalized entropy has been formulated that reduces to different known entropies for suitable limits of the parameters. Based on such four parameter generalized entropy (symbolized by $S_\mathrm{g}$), in the present paper, we examine the universe's evolution during its early phase, particularly from inflation to reheating, in the context of entropic cosmology where the entropic energy density acts as the inflaton. It turns out that the entropic energy successfully drives an early inflationary phase with a graceful exit, and moreover, the theoretical expectations of the observable indices get consistent with the recent Planck data for suitable ranges of the entropic parameters. After the inflation ends, the universe enters to a reheating stage when the entropic energy decays to relativistic particles with a certain decay rate. Actually the presence of the entropic parameters in the $S_\mathrm{g}$ ensures a continuous evolution of the Hubble parameter from a quasi de-Sitter phase during the inflation to a power law phase during the reheating stage dominated by a constant EoS parameter. Consequently we investigate the reheating phenomenology, and scan the entropic parameters from both the inflation and reheating requirements. We further address the possibility of instantaneous reheating in the present context of generalized entropy.

##### 2.Upgraded waveform model of eccentric binary black hole based on effective-one-body-numerical-relativity for spin-aligned binary black holes

**Authors:**Xiaolin Liu, Zhoujian Cao, Lijing Shao

**Abstract:** Effective one body numerical relativity waveform models for spin aligned binary black holes (SEOBNR) are based on the effective one body theoretical framework and numerical relativity simulation results. SEOBNR models have evolved through version 1 to version 4. We recently extended SEOBNRv1 model to SEOBNRE (Effective One Body Numerical Relativity waveform models for Spin aligned binary black holes along Eccentric orbit) model which is also valid for spin aligned binary black hole coalescence along eccentric orbit. In this paper we update our previous SEOBNRE model to make it consistent to SEOBNRv4 which is the most widely used SEOBNR waveform model. This upgraded SEOBNRE model improves accuracy compared to previous SEOBNRE model, especially for highly spinning black holes. For spin aligned binary black holes with mass ratio $1\leq q\lesssim10$, dimensionless spin $-0.9\lesssim\chi\lesssim0.995$ and orbital eccentricity $0\leq e_0\lesssim0.6$ at reference frequency $Mf_0=0.002$ ($M$ is the total mass of the binary black hole, $f_0\approx 40\frac{10{\rm M}_\odot}{M}$Hz), the upgraded SEOBNRE model can always fit numerical relativity waveform better than 98.2\%. For most cases the fitting factor can even be better than 99\%.

##### 3.Quintessential $α$-attractor inflation: A dynamical systems analysis

**Authors:**Artur Alho, Claes Uggla

**Abstract:** The equations for quintessential $\alpha$-attractor inflation with a single scalar field, radiation and matter in a spatially flat FLRW spacetime are recast into a regular dynamical system on a compact state space. This enables a complete description of the solution space of these models. The inflationary attractor solution is shown to correspond to the unstable center manifold of a de Sitter fixed point, and we describe connections between slow-roll and dynamical systems approximations for this solution, including Pad\'e approximants. We also introduce a new method for systematically obtaining initial data for quintessence evolution by using dynamical systems properties; in particular, this method exploits that there exists a radiation dominated line of fixed points with an unstable quintessence attractor submanifold, which plays a role that is reminiscent of that of the inflationary attractor solution for inflation.

##### 4.Polyhomogeneous spin-0 fields in Minkowski spacetime

**Authors:**Edgar Gasperin

**Abstract:** The asymptotic behaviour of massless spin-0 fields close to spatial and null infinity in Minkowski spacetime is studied by means of Friedrich's cylinder at spatial infinity. The results are applied to a system of equations called the good-bad-ugly which serves as a model for the Einstein field equations in generalised harmonic gauge. The relation between the logarithmic terms (polyhomogeneity) appearing in the solution obtained using conformal methods and those obtained by means of a heuristic method based on H\"ormander's asymptotic system is discussed. This review article is based on Class. Quantum Grav. 40 055002 and arXiv:2304.11950.

##### 5.Spherical particle orbits around a rotating black hole in massive gravity

**Authors:**Mohsen Fathi, J. R. Villanueva, Norman Cruz

**Abstract:** In this paper, we present a rotating de Rham-Gabadadze-Tolley black hole with a positive cosmological constant in massive gravity, achieved by applying a modified Newman-Janis algorithm. The black hole exhibits stable orbits of constant radii, prompting a numerical study on the behavior of the solutions to a nonic equation governing the radii of planar orbits around the black hole. Additionally, we investigate the stability of orbits near the event horizon and provide a comprehensive analytical examination of the solutions to the angular equations of motion. This is followed by simulating some spherical particle orbits around the black hole.

##### 6.Matching slowly rotating spacetimes split by dynamic thin shells

**Authors:**Jonas P. Pereira, Jorge A. Rueda

**Abstract:** We investigate within the Darmois-Israel thin shell formalism the match of neutral and asymptotically flat, slowly rotating spacetimes (up to the second order in the rotation parameter) when their boundaries are dynamic. It has several important applications in general relativistic systems, such as black holes and neutron stars, which we exemplify. We mostly focus on stability aspects of slowly rotating thin shells in equilibrium and surface degrees of freedom on the hypersurfaces splitting the matched slowly rotating spacetimes, e.g., surface energy density and surface tension. We show that the stability upon perturbations in the spherically symmetric case automatically implies stability in the slow rotation case. In addition, we show that when matching slowly rotating Kerr spacetimes through thin shells in equilibrium, surface degrees of freedom can decrease compared to their Schwarzschild counterparts, meaning that energy conditions could be weakened. Frame-dragging aspects of the match of slowly rotating spacetimes are also briefly discussed.

##### 7.Finiteness of quantum gravity with matter on a PL spacetime

**Authors:**Aleksandar Mikovic

**Abstract:** We study the convergence of the path integral for General Relativity with matter on a picewise linear (PL) spacetime that corresponds to a triangulation of a smooth manifold by using a path-integral measure that renders the pure gravity path integral finite. This measure depends on a parameter p, and in the case when the matter content is just scalar fields, we show that the path integral is absolutely convergent for p > 0,5 and not more than 2 scalar fields. In the case of Yang-Mills fields, we show that the path integral is absolutely convergent for the U(1) group and p > 0,5. In the case of Dirac fermions, we show that the path integral is absolutely convergent for any number of fermions and a sufficiently large p. When the matter content is given by scalars, Yang-Mills fields and fermions, as in the case of the Standard Model, we show that the path integral is absolutely convergent for p > 46,5. Hence one can construct a finite quantum gravity theory on a PL spacetime such that the classical limit is General Relativity coupled to the Standard Model.

##### 8.Large Inflationary Logarithms in a Nontrivial Nonlinear Sigma Model

**Authors:**C. Litos, R. P. Woodard, B. Yesilyurt

**Abstract:** Loops of inflationary gravitons are known to induce large temporal and spatial logarithms which can cause perturbation theory to break down. Nonlinear sigma models possess the same kind of derivative interactions and induce the same sorts of large logarithms, without the complicated index structure and potential gauge problem. Previous studies have examined models with zero field space curvature which can be reduced to free field theories by local, invertible field redefinitions. Here we study a model which cannot be so reduced and still shows the same sorts of large logarithms. We compute the evolution of the background at 1-loop and 2-loop orders, and we find the 1-loop $\beta$ and $\gamma$ functions.

##### 9.Quantum phenomena inside a black hole: quantization of the scalar field iniside horizon in Schwarzschild spacetime

**Authors:**Pawel Gusin, Andrzej Radosz, Andy T. Augousti, Janos Polonyi, Oleg B. Zaslavskii, Romuald J. 'Sciborski

**Abstract:** We discuss the problem of the quantization and dynamic evolution of a scalar free field in the interior of a Schwarzschild black hole. A unitary approach to the dynamics of the quantized field is proposed: a time-dependent Hamiltonian governing the Heisenberg equations is derived. It is found that the system is represented by a set of harmonic oscillators coupled via terms corresponding to the creation and annihilation of pairs of particles and that the symmetry properties of the spacetime, homogeneity and isotropy are obeyed by the coupling terms in the Hamiltonian. It is shown that Heisenberg equations for annihilation and creation operators are transformed into ordinary differential equations for appropriate Bogolyubov coefficients. Such a formulation leads to a general question concerning the possibility of gravitationally driven instability, that is however excluded in this case.

##### 10.Status of the GINGER project

**Authors:**Angela D. V. Di Virgilio
on behalf of GINGER Collaboration

**Abstract:** Large frame Ring laser gyroscopes, based on the Sagnac effect, are top sensitivity instrumentation to measure angular velocity with respect to the fixed stars. GINGER (Gyroscopes IN GEneral Relativity) project foresees the construction of an array of three large dimension ring laser gyroscopes, rigidly connected to the Earth. GINGER has the potentiality to measure general relativity effects and Lorentz Violation in the gravity sector, once a sensitivity of $10^{-9}$, or better, of the Earth rotation rate is obtained. Being attached to the Earth crust, the array will also provide useful data for geophysical investigation. For this purpose, it is at present under construction as part of the multi-components observatory called Underground Geophysics at Gran Sasso (UGSS). Sensitivity is the key point to determine the relevance of this instrument for fundamental science. The most recent progress in the sensitivity measurement, obtained on a ring laser prototype called GINGERINO, indicates that GINGER should reach the level of 1 part in $10^{11}$ of the Earth rotation rate.

##### 11.Probing internal dissipative processes of neutron stars with gravitational waves during the inspiral of neutron star binaries

**Authors:**Justin L. Ripley, Abhishek Hegade K. R., Nicolas Yunes

**Abstract:** We study the impact of out-of-equilibrium, dissipative effects on the dynamics of inspiraling neutron stars. We find that modeling dissipative processes (such as those from the stars internal effective fluid viscosity) requires that one introduce a new tidal deformability parameter--the dissipative tidal deformability--which modifies the phase of gravitational waves emitted during the inspiral phase of a neutron star binary. We show that the dissipative tidal deformability corrects the gravitational-wave phase at 4 post-Newtonian order for quasi-circular binaries. This correction receives a large finite-size enhancement by the stellar compactness, analogous to the case of the tidal deformability. Moreover, the correction is not degenerate with the time of coalescence, which also enters at 4PN order, because it contains a logarithmic frequency-dependent contribution. Using a simple Fisher analysis, we show that physically allowed values for the dissipative tidal deformability may be constrained by measurements of the phase of emitted gravitational waves to roughly the same extent as the (electric-type, quadrupolar) tidal deformability. Finally, we show that there are no out-of-equilibrium, dissipative corrections to the tidal deformability itself. We conclude that there are at least two relevant tidal deformability parameters that can be constrained with gravitational-wave phase measurements during the late inspiral of a neutron star binary: one which characterizes the adiabatic tidal response of the star, and another which characterizes the leading-order out-of-equilibrium, dissipative tidal response. These findings open a window to probe dissipative processes in the interior of neutron stars with gravitational waves.

##### 1.Detecting anisotropies of the stochastic gravitational wave background with TianQin

**Authors:**Kun Zhou, Jian-dong Zhang, Jun Cheng, Liangliang Ren

**Abstract:** The investigation of the anisotropy of the stochastic gravitational wave background (SGWB) using the TianQin detector plays a crucial role in studying the early universe and astrophysics. In this work, we examine the response of the $AET$ channel of the TianQin Time Delay Interferometry (TDI) to the anisotropy of the SGWB. We calculate the corresponding angular sensitivity curves and find that TianQin is capable of detecting the anisotropy of the SGWB, with an angular sensitivity reaching $10^{-10}$ for quadrupoles. Due to the fixed $z$-axis of TianQin pointing towards J0806, its overlap reduction functions (ORFs) exhibit specific symmetries, enabling the resolution of different multipole moments $\ell m$. The detection sensitivity is optimal for the $(2, 0)$ mode, with a sensitivity reaching $10^{-10}$. Using the Fisher matrix approach, we estimate the parameters and find that in the power-law spectrum model, higher logarithmic amplitudes lead to more effective reconstruction of the spectral index for all multipole moments. Under the optimal scenario with a signal amplitude of $\Omega_{\mathrm{GW}} (f = f_{\mathrm{c}}) h^2 = 10^{-9}$, the spectral indices can be reconstructed with uncertainties of $10^{-3}$, $10$, and $10^{-3}$ for $\ell = 0$, $1$, and $2$ multipole moments, respectively. For the cases of $(\ell, m) = (0, 0)$, $(1, 1)$, $(2, 0)$, and $(2, 2)$, the spectral indices can be reconstructed with uncertainties of $10^{-3}$, $10$, $10^{-3}$, and $10$, respectively.

##### 2.Black Hole Menagerie, Charged/Dyonic BHs and Radiation from Interacting Dyonic BH Pairs

**Authors:**Patrick Das Gupta, Mohd. Sirtaz

**Abstract:** We describe charged BHs, Penrose process for energy extraction from Kerr BHs and Wald's proposal concerning a Kerr BH slowly becoming a Kerr-Newman BH in the presence of a uniform magnetic field. In the context of BHs bearing magnetic charge, we discuss both magnetic monopoles as well as dyons, and their emergence from various models like string theory, GUTs and electroweak theories, etc. In the later portions, we concentrate on our recent research work pertaining to the non-relativistic dynamics of dyon-dyon interaction that includes mutual gravitational attraction. From the derived classical equations of motion, we obtain not only the well known Schwinger-Zwanziger quantization condition for dyons using Saha's argument based on quantized angular momentum of electromagnetic field but also a scalar virial theorem for an astrophysical system consisting of point particles, some of which carry both electric and magnetic charges. In the final sections, we obtain expressions for the generated electromagnetic wave as well as gravitational wave amplitudes, and the corresponding luminosities due to dyon-dyon interactions. Lastly, we discuss the results after computing these quantities using a range of values for the mass, electric and magnetic charges, etc. of the dyonic BHs.

##### 3.Observational Constraints on Hybrid Scale Factor in f(Q,T) Gravity with Anisotropic Space-Time

**Authors:**S. A. Narawade, M. Koussour, B. Mishra

**Abstract:** In this paper, we present an accelerating cosmological model by constraining the free parameters using the cosmological datasets in an extended symmetric teleparallel gravity for the flat and anisotropic space-time. We employ a time variable deceleration parameter that behaves early deceleration and late time acceleration in the form of Hybrid Scale Factor (HSF). We obtain the present values of deceleration parameter and analyse the late time behavior of the Universe based on the best-fit values of free parameters. We derive the dynamical parameters of the model and obtain the equation of state parameter at present in the quintessence region; however at late time it approaches to $\Lambda$CDM. The energy conditions are also analysed to validate the modified gravity and we find that strong energy condition is violating. We establish the importance of hybrid scale factor in the late time cosmic phenomena issue.

##### 4.Exact rotating wormholes via Ehlers transformations

**Authors:**Adolfo Cisterna, Keanu Müller, Konstantinos Pallikaris, Adriano Viganò

**Abstract:** In this paper, we construct exact rotating wormholes using Ehlers solution-generating technique. This is based on the Ernst description of four-dimensional, stationary, and axially symmetric solutions of the Einstein-Maxwell theory. We adopt the static Barcel\'o-Visser wormhole derived from the Einstein-Maxwell-conformal-scalar theory as a seed, and demonstrate, through the Ernst approach, how to construct two novel geometries of rotating wormholes. These geometries correspond to the Barcel\'o-Visser wormhole embedded within a rotating and a magnetic background, respectively. In the first case, the rotation is a result of a dragging force (due to the rotating background) acting on the initial static wormhole, while in the second case it is caused by the electromagnetic interaction between the electric charge of the static wormhole and the external magnetic field. We conduct a comprehensive analysis of the geometric properties of these configurations, and examine the new features introduced by rotation, such as the emergence of ergoregions. Recent evidence suggests that incorporating slow rotation can stabilise wormholes, rendering these exact, fully rotating solutions particularly appealing.

##### 5.Equations of state of shear-free Locally Rotationally Symmetric perfect fluid self-gravitating systems

**Authors:**Jonathan Hakata, Rituparno Goswami, Chevarra Hansraj, Sunil D. Maharaj

**Abstract:** In this paper, via a covariant semitetrad spacetime decomposition, we present a novel geometrical classification of shear-free Locally Rotationally Symmetric (LRS-II) perfect fluid self-gravitating systems, in terms of the covariantly defined fluid acceleration and the fluid expansion. We further analyze the interesting class of these systems that are dynamic, necessarily inhomogeneous with tidal deformations and yet shear-free. We deduce the governing highly non-linear differential equation that gives the possible equations of state of matter that can lead to such a scenario. We find that the possible equations of state are very limited.

##### 6.Tidal heating as a direct probe of Strangeness inside Neutron stars

**Authors:**Suprovo Ghosh, Bikram Keshari Pradhan, Debarati Chatterjee

**Abstract:** The cores of neutron stars (NS) reach densities several times the nuclear saturation density and could contain strangeness containing exotic particles such as hyperons. During the binary inspiral, viscous processes inside the NS matter can damp out the tidal energy induced by the companion and convert this to thermal energy to heat up the star. We demonstrate that the bulk viscosity originating from the non-leptonic weak interactions involving hyperons is several orders of magnitude higher than the standard neutron matter shear viscosity in the relevant temperature range of $10^6-10^9$K and for heavier mass NSs ($M \geq 1.6M_{\odot}$) that contain a significant fraction of hyperons in their core, the bulk viscosity can heat up the stars upto $0.1 - 1$ MeV before the final merger. This "tidal heating" process also introduces a net phase shift of $10^{-3}-0.5$ rad, depending on the component mass, in the gravitational wave (GW) signal that can potentially be detected using current and future generation GW detectors. Such a detection would be the direct confirmation of the presence of hyperons inside the NS core, having a great significance for the study of dense matter under extreme condition.

##### 7.Fab-Four cosmography to tackle the Hubble tension

**Authors:**Celia Escamilla-Rivera, José María de Albornoz-Caratozzolo, Sebastián Nájera

**Abstract:** In the context of the Fab-Four theory of gravity in a Friedmann-Lema\^itre-Robertson-Walker background, in this work we use the cosmography approach to study a particular self-tuning filter solution focused on a zero-curvature fixed point to study the $H_0$ tension. In this scheme, the equations restrict the universe's evolution to certain scenarios, including radiation-like expansion, matter-like expansion, and late-time acceleration. Furthermore, we build the cosmographic series of the Fab-Four theory to obtain the kinematic parameters as the Hubble constant $H_0$ and the deceleration parameter $q_0$ for all the scenarios mentioned. Finally, we compare our results to find that it is possible to alleviate the current discrepancy on $H_0$ by considering specific requirements on the free parameters of the Fab-Four theory through a self-tuning filter.

##### 1.Cosmology of $f(Q)$ gravity in non-flat Universe

**Authors:**Hamid Shabani, Avik De, Tee-How Loo, Emmanuel N. Saridakis

**Abstract:** We investigate the cosmological implications of $f(Q)$ gravity, which is a modified theory of gravity based on non-metricity, in non-flat geometry. We perform a detailed dynamical-system analysis keeping the $f(Q)$ function completely arbitrary. As we show, the cosmological scenario admits a dark-matter dominated point, as well as a dark-energy dominated de Sitter solution which can attract the Universe at late times. However, the main result of the present work is that there are additional critical points which exist solely due to curvature. In particular, we find that there are curvature-dominated accelerating points which are unstable and thus can describe the inflationary epoch. Additionally, there is a point in which the dark-matter and dark-energy density parameters are both between zero and one, and thus it can alleviate the coincidence problem. Finally, there is a saddle point which is completely dominated by curvature. In order to provide a specific example, we apply our general analysis to the power-law case, showing that we can obtain the thermal history of the Universe, in which the curvature density parameter may exhibit a peak at intermediate times. These features, alongside possible indications that non-zero curvature could alleviate the cosmological tensions, may serve as advantages for $f(Q)$ gravity in non-flat geometry.

##### 2.Constraining Quadratic $f(R)$ Gravity from Astrophysical Observations of the Pulsar J0704+6620

**Authors:**G. G. L. Nashed, Waleed El Hanafy

**Abstract:** We apply quadratic $f(R)=R+\epsilon R^2$ field equations, where $\epsilon$ has a dimension [L$^2$], to static spherical stellar model. We assume the interior configuration is determined by Krori-Barua ansatz and additionally the fluid is anisotropic. Using the astrophysical measurements of the pulsar PSR J0740+6620 as inferred by NICER and XMM observations, we determine $\epsilon\approx \pm 3$ km$^2$. We show that the model can provide a stable configuration of the pulsar PSR J0740+6620 in both geometrical and physical sectors. We show that the Krori-Barua ansatz within $f(R)$ quadratic gravity provides semi-analytical relations between radial, $p_r$, and tangential, $p_t$, pressures and density $\rho$ which can be expressed as $p_r\approx v_r^2 (\rho-\rho_1)$ and $p_r\approx v_t^2 (\rho-\rho_2)$, where $v_r$ ($v_t$) is the sound speed in radial (tangential) direction, $\rho_1=\rho_s$ (surface density) and $\rho_2$ are completely determined in terms of the model parameters. These relations are in agreement with the best-fit equations of state as obtained in the present study. We further put the upper limit on the compactness, which satisfies the $f(R)$ modified Buchdahl limit. Interestingly, the quadratic $f(R)$ gravity with negative $\epsilon$ naturally restricts the maximum compactness to values lower than Buchdahl limit, unlike the GR or $f(R)$ gravity with positive $\epsilon$ where the compactness can arbitrarily approach the black hole limit $C\to 1$. The model predicts a core density a few times the saturation nuclear density $\rho_{\text{nuc}} = 2.7\times 10^{14}$ g/cm$^3$, and a surface density $\rho_s > \rho_{\text{nuc}}$. We provide the mass-radius diagram corresponding to the obtained boundary density which has been shown to be in agreement with other observations.

##### 3.Cosmological Perturbations in the Teleparallel analog of Horndeski gravity

**Authors:**Bobomurat Ahmedov, Konstantinos F. Dialektopoulos, Jackson Levi Said, Abdurakhmon Nosirov, Odil Yunusov, Zinovia Oikonomopoulou

**Abstract:** In this work we study the cosmological perturbations in Bahamonde-Dialektopoulos-Levi Said (BDLS) theory, i.e. the teleparallel analog of Horndeski gravity. In order to understand the evolution of structure in a cosmological model, it is necessary to study its cosmology not only in the background but also perturbatively. Both Horndeski and its teleparallel analog have been analyzed a lot in the literature, but in order to study them quantitatively, we need to know their cosmological perturbations. That is why, we study here the scalar-vector-tensor decomposition of the theory and we also express the so-called alpha parameters in terms of the arbitrary functions of the theory, that designate the deviation from the {\Lambda}CDM model. We have explored tensor, vector and scalar perturbation of the action up to second order, which drastically opens up new possibilities on searches in the parameter space of scalar-tensor theories in the context of observations.

##### 4.Testing gravity with cosmic variance-limited pulsar timing array correlations

**Authors:**Reginald Christian Bernardo, Kin-Wang Ng

**Abstract:** The nanohertz stochastic gravitational wave background (SGWB) is an excellent early universe laboratory for testing the fundamental properties of gravity. In this letter, we elucidate on the full potential of pulsar timing array (PTA) by utilizing cosmic variance-limited, or rather experimental noise-free, correlation measurements to understand the SGWB and by extension gravity. We show that measurements of the angular power spectrum play a pivotal role in the PTA precision era for scientific inferencing. In particular, we illustrate that cosmic variance-limited measurements of the first few power spectrum multipoles enable us to clearly set apart general relativity from alternative theories of gravity.

##### 5.Addressing issues in defining the Love number for black holes

**Authors:**Rajendra Prasad Bhatt, Sumanta Chakraborty, Sukanta Bose

**Abstract:** We present an analytic method for calculating the tidal response function of a non-rotating and a slowly rotating black hole from the Teukolsky equation in the small frequency and the near horizon limit. We point out that in the relativistic context, there can be two possible definitions of the tidal Love number and the dissipative part that arise from the tidal response function. Our results suggest that both of these definitions predict zero tidal Love number for a non-rotating black hole. On the other hand, for a slowly rotating black hole in a generic tidal environment, these two definitions of the tidal Love number do not coincide. While one procedure suggests a zero tidal Love number, the other procedure gives a purely imaginary tidal Love number. As expected, the dissipative terms differ as well. We emphasize that in our analysis we keep all the terms linear in the frequency, unlike previous works in the literature. Following this, we propose a procedure to calculate the tidal response function and hence the Love number for an arbitrarily rotating black hole.

##### 1.Recovery of consistency in thermodynamics of regular black holes in Einstein's gravity coupled with nonlinear electrodynamics

**Authors:**Yang Guo, Hao Xie, Yan-Gang Miao

**Abstract:** As one of candidate theories in the construction of regular black holes, Einstein's gravity coupled with nonlinear electrodynamics has been a topic of great concerns. Owing to the coupling between Einstein's gravity and nonlinear electrodynamics, we need to reconsider the first law of thermodynamics, which will lead to a new thermodynamic phase space. In such a phase space, the equation of state accurately describes the complete phase transition process of regular black holes. The Maxwell equal area law strictly holds when the phase transition occurs, and the entropy obeys the Bekenstein-Hawking area formula, which is compatible with the situation in Einstein's gravity.

##### 2.Curved spacetime as a dispersive multiferroic medium for an electromagnetic wave: polarization and magnetization vectors in the Schwarzschild spacetime

**Authors:**Bobur Turimov, Igor Smolyaninov

**Abstract:** We study one of the interesting properties of the electromagnetic wave propagation in the curved Schwarzschild background spacetime in the framework of general relativity (GR). The electromagnetic wave equation has been derived from vacuum general relativistic Maxwell's equations. It is shown that the solutions for the electromagnetic field can be expanded in the spherical harmonic functions and all components of the electromagnetic fields can be expressed in terms of two radial profile functions. These radial profile functions can be expressed in terms of the confluent Heun function. The calculated behaviour of the electric and magnetic susceptibilities near the event horizon appears to be similar to the susceptibilities of multiferroic materials near phase transition. The Curie temperature of this phase transition appears to coincide with the Hawking temperature.

##### 3.Glued massive particles surfaces

**Authors:**Igor Bogush, Kirill Kobialko, Dmitri Gal'tsov

**Abstract:** A novel generalization of photon surfaces to the case of massive charged particles is given for spacetimes with at least one isometry, including stationary ones. A related notion of glued massive particle surfaces is also defined. These surfaces join worldlines parametrized by a family of independent conserved quantities and naturally arise in integrable spacetimes. We describe the basic geometric properties of such surfaces and their relationship to slice-reducible Killing tensors, illustrating all concepts with a number of examples. Massive particle surfaces have potential applications in the context of uniqueness theorems, Penrose inequalities, integrability, and the description of black-hole shadows in streams of massive charged particles or photons in a medium with an effective mass and charge.

##### 4.A Pamphlet against The Energy

**Authors:**Alexey Golovnev

**Abstract:** It is a well-known fact that there is no well-defined notion of conserved energy in gravity. In my opinion, it is not a big deal. As a conserved quantity, energy is a rather artificial invention which works perfectly well as long as we have a natural symmetry with respect to translations in time, however not when there ceases to be any notion of an objective time, rather than a mere coordinate. However, recently we have got an essential progress in teleparallel models of gravity, with emerging opinions of having solved the problem of energy. I explain why I think it simply makes no good sense to go for solving a non-existent problem, and the correct answer is just that in general there is no such thing as The Energy. (It has just been presented online at the Conference on Geometric Foundations of Gravity 2023 in Tartu, Estonia.)

##### 5.Waveform systematics in identifying gravitationally lensed gravitational waves: Posterior overlap method

**Authors:**Ángel Garrón, David Keitel

**Abstract:** Gravitational lensing has been extensively observed for electromagnetic signals, but not yet for gravitational waves (GWs). Detecting lensed GWs will have many astrophysical and cosmological applications, and becomes more feasible as the sensitivity of the LIGO-Virgo-KAGRA detectors improves. One of the missing ingredients to robustly identify lensed GWs is to ensure that the statistical tests used are robust under the choice of underlying waveform models. We present the first systematic study of possible waveform systematics in identifying candidates for strongly lensed GW event pairs, focusing on the posterior overlap method. To this end, we compare Bayes factors from all posteriors using different waveforms included in GWTC data releases from the first three observing runs (O1-O3). We find that waveform choice yields a wide spread of Bayes factors in some cases. However, it is likely that no event pairs from O1 to O3 were missed due to waveform choice. We also perform parameter estimation with additional waveforms for interesting cases, to understand the observed differences. We also briefly explore if computing the overlap from different runs for the same event can be a useful metric for waveform systematics or sampler issues, independent of the lensing scenario.

##### 6.Numerical convergence of model Cauchy-Characteristic Extraction and Matching

**Authors:**Thanasis Giannakopoulos, Nigel T. Bishop, David Hilditch, Denis Pollney, Miguel Zilhão

**Abstract:** Gravitational waves provide a powerful enhancement to our understanding of fundamental physics. To make the most of their detection we need to accurately model the entire process of their emission and propagation toward interferometers. Cauchy-Characteristic Extraction and Matching are methods to compute gravitational waves at null infinity, a mathematical idealization of detector location, from numerical relativity simulations. Both methods can in principle contribute to modeling by providing highly accurate gravitational waveforms. An underappreciated subtlety in realising this potential is posed by the (mere) weak hyperbolicity of the particular PDE systems solved in the characteristic formulation of the Einstein field equations. This shortcoming results from the popular choice of Bondi-like coordinates. So motivated, we construct toy models that capture that PDE structure and study Cauchy-Characteristic Extraction and Matching with them. Where possible we provide energy estimates for their solutions and perform careful numerical norm convergence tests to demonstrate the effect of weak hyperbolicity on Cauchy-Characteristic Extraction and Matching. Our findings strongly indicate that, as currently formulated, Cauchy-Characteristic Matching for the Einstein field equations would provide solutions that are, at best, convergent at an order lower than expected for the numerical method, and may be unstable. In contrast, under certain conditions, the Extraction method can provide properly convergent solutions. Establishing however that these conditions hold for the aforementioned characteristic formulations is still an open problem.

##### 7.Spacetime metric from quantum-gravity corrected Feynman propagators

**Authors:**P. Fernandez de Cordoba, J. M. Isidro, Rudranil Roy

**Abstract:** Differentiation of the scalar Feynman propagator with respect to the spacetime coordinates yields the metric on the background spacetime that the scalar particle propagates in. Now Feynman propagators can be modified in order to include quantum-gravity corrections as induced by a zero-point length $L>0$. These corrections cause the length element $\sqrt{s^2}$ to be replaced with $\sqrt{s^2 + 4L^2}$ within the Feynman propagator. In this paper we compute the metrics derived from both the quantum-gravity free propagators and from their quantum-gravity corrected counterparts. We verify that the latter propagators yield the same spacetime metrics as the former, provided one measures distances greater than the quantum of length $L$. We perform this analysis in the case of the background spacetime $\mathbb{R}^D$ in the Euclidean sector.

##### 1.Reconstruction of $Λ$CDM Universe from Noether symmetries in Chameleon gravity

**Authors:**Andronikos Paliathanasis

**Abstract:** We apply the Noether symmetries to constrain the unknown functions of chameleon gravity in the cosmological scenario of a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker space-time with an ideal gas. For this gravitational model the field equations admit a point-like Lagrangian with as unknown functions the scalar field potential and the coupling function which is responsible for the chameleon mechanism. Noether's first theorem provides us with four sets of closed-form functional forms for which variational symmetries exist. We construct the corresponding conservation laws and we use them in order to determine new analytic solutions in chameleon gravity. From the analysis of the physical properties of the new solution it follows that in the late universe they can reproduce the $\Lambda$CDM model without having to assume the presence of a pressureless fluid in the cosmological fluid.

##### 2.Extracting spinning wormhole energy via magnetic reconnection

**Authors:**Xu Ye, Chao-Hui Wang, Shao-Wen Wei

**Abstract:** Magnetic reconnection has been extensively shown to be a promising approach to extract spinning black hole energy. In this paper, we focus on extracting spinning wormhole energy via such mechanism. The study shows that it is indeed possible to extract rotating energy from a spinning wormhole with small regularization parameter $\ell$ of the central singularity. The efficiency and power of the energy extraction are also evaluated. Quite different from the Kerr black hole, the spin of the wormhole can take arbitrarily large value. However, the increasing of wormhole spin not always improves the efficiency and power of energy extraction. By further comparing with the Kerr black hole, we find the wormhole is more efficient when the magnetic reconnection happens within radial distance $r/M<1$. These studies reveal the features of extracting spinning wormhole energy, and more underlying properties are expected to be disclosed for the horizonless objects.

##### 3.Acoustic Kerr Metric in Analogue Gravity

**Authors:**Deeshani Mitra, Surojit Dalui, Subir Ghosh, Arpan Krishna Mitra

**Abstract:** The present paper is based on a previous work (involving two of the present authors) where a generalized fluid dynamical model was proposed. The underlying symplectic structure of the Lagrangian discrete degrees of freedom obeyed a Non-Commutative algebra, generated by Berry curvature correction. In an Euler (or Hamiltonian) framework, this is manifested as an extended algebra between the fluid variables, leading to the extended fluid model. Here we study the dynamics of sonic fluctuations that live in this effective analogue gravity spacetime. Interestingly enough, the effective metric resembles that of a spinning Black Hole; the spin is induced by the underlying Non-Commutative structure. The effective mass and spin parameters of the Black Hole, in terms of fluid parameters, are also identified. The connection of our model with anomalous Hall systems may lead to observable signatures of the analogue black hole in physical systems.

##### 4.Practical approaches to analyzing PTA data: Cosmic strings with six pulsars

**Authors:**Hippolyte Quelquejay Leclere, Pierre Auclair, Stanislav Babak, Aurélien Chalumeau, Danièle A. Steer, J. Antoniadis, A. -S. Bak Nielsen, C. G. Bassa, A. Berthereau, M. Bonetti, E. Bortolas, P. R. Brook, M. Burgay, R. N. Caballero, D. J. Champion, S. Chanlaridis, S. Chen, I. Cognard, G. Desvignes, M. Falxa, R. D. Ferdman, A. Franchini, J. R. Gair, B. Goncharov, E. Graikou, J. -M. Grießmeier, L. Guillemot, Y. J. Guo, H. Hu, F. Iraci, D. Izquierdo-Villalba, J. Jang, J. Jawor, G. H. Janssen, A. Jessner, R. Karuppusamy, E. F. Keane, M. J. Keith, M. Kramer, M. A. Krishnakumar, K. Lackeos, K. J. Lee, K. Liu, Y. Liu, A. G. Lyne, J. W. McKee, R. A. Main, M. B. Mickaliger, I. C. Niţu, A. Parthasarathy, B. B. P. Perera, D. Perrodin, A. Petiteau, N. K. Porayko, A. Possenti, A. Samajdar, S. A. Sanidas, A. Sesana, G. Shaifullah, L. Speri, R. Spiewak, B. W. Stappers, S. C. Susarla, G. Theureau, C. Tiburzi, E. van der Wateren, A. Vecchio, V. Venkatraman Krishnan, J. P. W. Verbiest, J. Wang, L. Wang, Z. Wu

**Abstract:** We search for a stochastic gravitational wave background (SGWB) generated by a network of cosmic strings using six millisecond pulsars from Data Release 2 (DR2) of the European Pulsar Timing Array (EPTA). We perform a Bayesian analysis considering two models for the network of cosmic string loops, and compare it to a simple power-law model which is expected from the population of supermassive black hole binaries. Our main strong assumption is that the previously reported common red noise process is a SGWB. We find that the one-parameter cosmic string model is slightly favored over a power-law model thanks to its simplicity. If we assume a two-component stochastic signal in the data (supermassive black hole binary population and the signal from cosmic strings), we get a $95\%$ upper limit on the string tension of $\log_{10}(G\mu) < -9.9$ ($-10.5$) for the two cosmic string models we consider. In extended two-parameter string models, we were unable to constrain the number of kinks. We test two approximate and fast Bayesian data analysis methods against the most rigorous analysis and find consistent results. These two fast and efficient methods are applicable to all SGWBs, independent of their source, and will be crucial for analysis of extended data sets.

##### 5.A direct correspondence between Newtonian gravitation and general relativity

**Authors:**Thomas Buchert

**Abstract:** We present a strategy to obtain equations of general relativity for an irrotational dust continuum within a flow-orthogonal foliation of spacetime from the equations of Newtonian gravitation, and vice versa, without employing a weak field expansion or a limiting process on the speed of light. We argue that writing Newton's equations in a Lagrangian frame and relaxing integrability of vector gradients is sufficient to obtain equations that are identical to Einstein's equations in 3+1 form when respecting the Lorentzian signature of the time-parametrization. We discuss implications and provide an outlook on how to extend the obtained correspondence to more general spacetimes.

##### 6.Incompatibility of gravity theories with auxiliary fields with the Standard Model

**Authors:**Giulia Ventagli, Paolo Pani, Thomas P. Sotiriou

**Abstract:** Theories of gravity with auxiliary fields are of particular interest since they are able to circumvent Lovelock's theorem while avoiding to introduce new degrees of freedom. This type of theories introduces derivatives of the stress-energy tensor in the modified Einstein equation. This peculiar structure of the field equations was shown to lead to spacetime singularities on the surface of stars. Here we focus on yet another problem afflicting gravity theories with auxiliary field. We show that such theories introduce deviations to the Standard Model unless one severely constrains the parameters of the theory, preventing them to produce significant phenomenology at large scales. We first consider the specific case of Palatini $f({\cal R})$ gravity, to clarify the results previously obtained in arXiv:astro-ph/0308111. We show that the matter fields satisfy the Standard Model field equations which reduce to those predicted by General Relativity in the local frame only at tree level, whereas at higher orders in perturbation theory they are affected by corrections that percolate from the gravity sector regardless of the specific $f({\cal R})$ model considered. Finally, we show that this is a more general issue affecting theories with auxiliary fields connected to the same terms responsible for the appearance of surface singularities.

##### 1.Demonstration of Machine Learning-assisted real-time noise regression in gravitational wave detectors

**Authors:**Muhammed Saleem, Alec Gunny, Chia-Jui Chou, Li-Cheng Yang, Shu-Wei Yeh, Andy H. Y. Chen, Ryan Magee, William Benoit, Tri Nguyen, Pinchen Fan, Deep Chatterjee, Ethan Marx, Eric Moreno, Rafia Omer, Ryan Raikman, Dylan Rankin, Ritwik Sharma, Michael Coughlin, Philip Harris, Erik Katsavounidis

**Abstract:** Real-time noise regression algorithms are crucial for maximizing the science outcomes of the LIGO, Virgo, and KAGRA gravitational-wave detectors. This includes improvements in the detectability, source localization and pre-merger detectability of signals thereby enabling rapid multi-messenger follow-up. In this paper, we demonstrate the effectiveness of \textit{DeepClean}, a convolutional neural network architecture that uses witness sensors to estimate and subtract non-linear and non-stationary noise from gravitational-wave strain data. Our study uses LIGO data from the third observing run with injected compact binary signals. As a demonstration, we use \textit{DeepClean} to subtract the noise at 60 Hz due to the power mains and their sidebands arising from non-linear coupling with other instrumental noise sources. Our parameter estimation study on the injected signals shows that \textit{DeepClean} does not do any harm to the underlying astrophysical signals in the data while it can enhances the signal-to-noise ratio of potential signals. We show that \textit{DeepClean} can be used for low-latency noise regression to produce cleaned output data at latencies $\sim 1-2$\, s. We also discuss various considerations that may be made while training \textit{DeepClean} for low latency applications.

##### 2.A study of the light bending phenomenon under full general relativity for a pulsar in a binary with a Schwarzschild black hole

**Authors:**Jyotijwal Debnath, Manjari Bagchi, Avishek Basu

**Abstract:** The values of the bending delays in the signal of a radio pulsar in a binary with a stellar mass black hole as a companion have been calculated accurately within a full general relativistic framework considering the Schwarzchid spacetime near the companion. The results match with the pre-existing approximate analytical expressions unless both of the orbital inclination angle and the orbital phase are close to $90^{\circ}$. For such a case, the approximate analytical expressions underestimate the value of the bending delay. On the other hand, for systems like the double pulsar, those expressions are valid throughout the orbital phase, unless its inclination angle is very close to 90 degrees. For a pulsar-black hole binary, the bending phenomenon also increases the strength of the pulse profile and sometimes can lead to a small low intensity tail.

##### 3.Relative Locality in curved spacetimes and event horizons

**Authors:**F. Mercati, J. J. Relancio

**Abstract:** In the past decade, significant efforts have been devoted to the study of Relative Locality, which aims to generalize the kinematics of relativistic particles to a nonlocal framework by introducing a nontrivial geometry for momentum space. This paper builds upon a recent proposal to extend the theory to curved spacetimes and investigates the behavior of horizons in certain spacetimes with this nonlocality framework. Specifically, we examine whether nonlocality effects weaken or destroy the notion of horizon in these spacetimes. Our analysis indicates that, in the chosen models, the nonlocality effects do not disrupt the notion of horizon and that it remains as robust as it is in General Relativity.

##### 4.Semiclassical Quadratic Gravity Revisited

**Authors:**Kostas Kleidis

**Abstract:** The semiclassical interaction of the gravitational with a quantum scalar field is considered, in view of the renormalizability of the associated energy-momentum tensor in a n-dimensional curved spacetime resulting from a quadratic gravitational lagrangian. It is shown that, in this case, a novel coupling between the square curvature term, ${\cal R}^2$, and the quantum field needs to be introduced. The interaction so considered, discards any higher-order derivative terms from the associated gravitational field equations, but, at the expense, it introduces a geometric source term in the wave equation for the quantum field. Unlike the conformal coupling case, this term does not represent an additional mass; hence, in quadratic gravity theories, quantum fields can interact with gravity in a more generic way and not only through their mass (or energy) content.

##### 5.On the gravitational diagram technique in the discrete setup

**Authors:**V. M. Khatsymovsky

**Abstract:** This article is in the spirit of our work on the consequences of the Regge calculus, where some edge length scale arises as an optimal initial point of the perturbative expansion after functional integration over connection. Now consider the perturbative expansion itself. To obtain an algorithmizable diagram technique, we consider the simplest periodic simplicial structure with a frozen part of the variables ("hypercubic"). After functional integration over connection, the system is described by the metric $g_{\lambda \mu}$ at the sites. We parameterize $g_{\lambda \mu}$ so that the functional measure becomes Lebesgue. The discrete diagrams are finite and reproduce (for ordinary, non-Planck external momenta) those continuum counterparts that are finite. We give the parametrization of $g_{\lambda \mu}$ up to terms, providing, in particular, additional three-graviton and two-graviton-two-matter vertices, which can give additional one-loop corrections to the Newtonian potential. The edge length scale is $\sim \sqrt{ \eta }$, where $\eta$ defines the free factor $ ( - \det \| g_{\lambda \mu} \| )^{ \eta / 2}$ in the measure and should be a large parameter to ensure the true action after integration over connection. We verify the important fact that the perturbative expansion does not contain increasing powers of $\eta$ if its initial point is chosen close enough to the maximum point of the measure, thus justifying this choice.

##### 6.Extended bodies with spin induced quadrupoles on circular equatorial orbits in Kerr spacetime

**Authors:**Iason Timogiannis, Georgios Lukes-Gerakopoulos, Theocharis A. Apostolatos

**Abstract:** This work discusses the motion of extended test bodies as described by the Mathisson-Papapetrou-Dixon (MPD) equations in the pole-dipole-quadrupole approximation. We focus on the case that the quadrupole is solely induced by the spin of the body which is assumed to move on a circular equatorial orbit in a Kerr background. To fix the center of mass of the MPD body we use two different spin supplementary conditions (SSCs): the Tulczyjew-Dixon SSC and the Mathisson-Pirani SSC. We provide the frequencies of the circular equatorial orbits for the pole-dipole-(spin induced) quadrupole approximation of the body for both SSCs. In the process we develop an explicit four-velocity four-momentum relation for a pole-dipole-quadrupole body under the Mathisson-Pirani SSC.

##### 7.A brief note on field equations in generalized theories of gravity

**Authors:**Jun-Jin Peng

**Abstract:** In the work [1](arXiv:1109.3846 [gr-qc]), to obtain a simple and economic formulation of field equations of generalised theories of gravity described by the Lagrangian $\sqrt{-g}L\big(g^{\alpha\beta},R_{\mu\nu\rho\sigma}\big)$, the equality $\big(\partial L/\partial g^{\mu\nu}\big)_{R_{\alpha\beta\kappa\omega}} =2R_{\mu}^{~\lambda\rho\sigma}P_{\nu\lambda\rho\sigma}$ was derived. In this short note, it is demonstrated that such an equality can be directly derived from an off-shell Noether current associated with an arbitrary vector. As a byproduct, a generalized Bianchi identity related to the divergence for the expression of field equations is obtained. The results reveal that using the Noether current to determine field equations even can avoid calculating the derivative of the Lagrangian density with respect to the metric. Besides, the analysis is extended to the Lagrangian including terms of the covariant derivative of the Riemann tensor.

##### 8.Cosmological coupling of nonsingular black holes

**Authors:**M. Cadoni, A. P. Sanna, M. Pitzalis, B. Banerjee, R. Murgia, N. Hazra, M. Branchesi

**Abstract:** We show that -- in the framework of general relativity (GR) -- if black holes (BHs) are singularity-free objects, they couple to the large-scale cosmological dynamics. We find that the leading contribution to the resulting growth of the BH mass ($M_{\rm BH}$) as a function of the scale factor $a$ stems from the curvature term, yielding $M_{\rm BH} \propto a^k$, with $k=1$. We demonstrate that such a linear scaling is universal for spherically-symmetric objects, and it is the only contribution in the case of regular BHs. For nonsingular horizonless compact objects we instead obtain an additional subleading model-dependent term. We conclude that GR nonsingular BHs/horizonless compact objects, although cosmologically coupled, are unlikely to be the source of dark energy. We test our prediction with astrophysical data by analysing the redshift dependence of the mass growth of supermassive BHs in a sample of elliptical galaxies at redshift $z=0.8 -0.9$. We also compare our theoretical prediction with higher redshift BH mass measurements obtained with the James Webb Space Telescope (JWST). We find that, while $k=1$ is compatible within $2\sigma$ with JWST results, the data from elliptical galaxies at $z=0.8 -0.9$ favour values of $k>1$. New samples of BHs covering larger mass and redshift ranges and more precise BH mass measurements are required to settle the issue.

##### 9.Generalized second law of thermodynamics in massive gravity

**Authors:**Mohammad Beigmohammadi, Kayoomars Karami

**Abstract:** Here, we study the generalized second law (GSL) of thermodynamics in the framework of massive gravity. To do this, we consider a FRW universe filled only with matter and enclosed by the apparent horizon. In addition, we consider two models including generalized massive gravity (GMG) as well as dRGT massive gravity on de Sitter. For both models, we first study the dynamics of background cosmology and then explore the validity of GSL. We conclude that for the selected values of model parameters the GSL is respected.

##### 10.Equivalence of matter-type modified gravity theories to general relativity with nonminimal matter interaction

**Authors:**Özgür Akarsu, Mariam Bouhmadi-López, Nihan Katırcı, Elham Nazari, Mahmood Roshan, N. Merve Uzun

**Abstract:** We show that gravity models, such as $f(\mathcal{L}_{\rm m})$, $f(g_{\mu\nu} T^{\mu\nu})$ and $f(T_{\mu\nu} T^{\mu\nu})$, that modify the introduction of the material source in the usual Einstein-Hilbert action by adding only matter-related terms to the matter Lagrangian density $\mathcal{L}_{\rm m}$ are equivalent to general relativity with nonminimal interactions. Through the redefinition $\mathcal{L}_{\rm m}+f \rightarrow \mathcal{L}_{\rm m}^{\rm tot}$, these models are exactly GR, yet the usual material field $T_{\mu\nu}$ and its accompanying partner, viz., the modification field $T_{\mu\nu}^{\rm mod}$ interact nonminimally. That is, $\nabla^{\mu}T_{\mu\nu}=-Q_{\nu}=-\nabla^{\mu}T_{\mu\nu}^{\rm mod}$, where $Q_{\nu}$ is the interaction kernel that governs the rate of energy transfer. We focus on the particular model, the energy-momentum squared gravity, where the usual material field $T_{\mu\nu}$ brings in an accompanying energy-momentum squared field , $T_{\mu\nu}^{\rm emsf}$ along with a sui generis nonminimal interaction between them. Compared to usual phenomenological nonminimal interaction models in the literature, EMSF gives rise to more intricate interaction kernels having covariant formulation even with simple forms of the $f$ function. We elaborate upon EMSF via some different aspects: a DE component induced from the interaction of sources such as cold dark matter and relativistic species with their accompanying EMSFs generating interacting DE-DM models, mimicking noncanonical scalar field, etc., or a Hoyle-type creation field generating steady-state universe models extended to fluids other than dust and a mimicker of modified generalized Chaplygin gas. We also demonstrate the proper calculation of second metric variation of $\mathcal{L}_{\rm m}$, as well as in models that contain scalars like $g_{\mu\nu} T^{\mu\nu}\,,R_{\mu\nu}T^{\mu\nu}$ and $G_{\mu\nu} T^{\mu\nu}$.

##### 11.Velocity dispersion of dark matter deficit ultra-diffuse galaxies: A case for modified gravity

**Authors:**Esha Bhatia, Sayan Chakrabarti, Sovan Chakraborty

**Abstract:** The line of sight velocity dispersion of the ultra-diffuse galaxies (UDGs) NGC1052-DF2 and NGC1052-DF4 have been reasonably explained only with the baryonic matter, without requiring any dark matter contribution. The comparable ratio between the baryonic and halo mass also ascertain the above claim for the two dark matter deficit galaxies. This paves the way for analyzing alternative gravity theories such as the $f(R)$ gravity and the Renormalization Group correction to General Relativity (RGGR). The analysis of the line of sight velocity dispersion shows that the choice of $f(R)$ gravity models such as Taylor expanded $f(R)$ about $R=0$ or a simple power law model of choice $R^n$ is consistent with the observational data. Similar statistical analysis is done for the RGGR and is also found to be a viable explanation for the observed velocity dispersion. We perform a global fit of the model parameters together with both the UDGs. The coupling parameters of the theories are considered as the global ones, and local variables such as the scale parameters are considered to be dependent on the individual galaxy.

##### 12.Gravitational Radiation from hyperbolic encounters in the presence of dark matter

**Authors:**Abhishek Chowdhuri, Rishabh Kumar Singh, Kaushik Kangsabanik, Arpan Bhattacharyya

**Abstract:** In this study, we look into binaries undergoing gravitational radiation during a hyperbolic passage. Such hyperbolic events can be a credible source of gravitational waves in future detectors. We systematically calculate fluxes of gravitational radiation from such events in the presence of dark matter, also considering the effects of dynamical friction. We also investigate the binary dynamics through the changes in the orbital parameters by treating the potential due to dark matter spike and the dynamical friction effects as a perturbation term. An insight into the effects of such a medium on the binaries from the corresponding osculating elements opens up avenues to study binary dynamics for such events.

##### 13.Towards a robust and reliable deep learning approach for detection of compact binary mergers in gravitational wave data

**Authors:**Shreejit Jadhav, Mihir Shrivastava, Sanjit Mitra

**Abstract:** The ability of deep learning (DL) approaches to learn generalised signal and noise models, coupled with their fast inference on GPUs, holds great promise for enhancing gravitational-wave (GW) searches in terms of speed, parameter space coverage, and search sensitivity. However, the opaque nature of DL models severely harms their reliability. In this work, we meticulously develop a DL model stage-wise and work towards improving its robustness and reliability. First, we address the problems in maintaining the purity of training data by deriving a new metric that better reflects the visual strength of the "chirp" signal features in the data. Using a reduced, smooth representation obtained through a variational auto-encoder (VAE), we build a classifier to search for compact binary coalescence (CBC) signals. Our tests on real LIGO data show an impressive performance of the model. However, upon probing the robustness of the model through adversarial attacks, its simple failure modes were identified, underlining how such models can still be highly fragile. As a first step towards bringing robustness, we retrain the model in a novel framework involving a generative adversarial network (GAN). Over the course of training, the model learns to eliminate the primary modes of failure identified by the adversaries. Although absolute robustness is practically impossible to achieve, we demonstrate some fundamental improvements earned through such training, like sparseness and reduced degeneracy in the extracted features at different layers inside the model. Through comparative inference on real LIGO data, we show that the prescribed robustness is achieved at practically zero cost in terms of performance. Through a direct search on ~8.8 days of LIGO data, we recover two significant CBC events from GWTC-2.1, GW190519_153544 and GW190521_074359, and report the search sensitivity.

##### 14.Comment on "Dark matter as a Weyl geometric effect''

**Authors:**Israel Quiros

**Abstract:** In this note we comment on a recent attempt by P. Burikham, T. Harko, K. Pimsamarn and S. Shahidi [Phys. Rev. D {\bf 107}, 064008 (2023)] to explain the galactic rotation curves as the result of the motion of time-like test particles in the Weyl geometric theory of gravity developed in [Eur. Phys. J. C {\bf 82}, 23 (2022)]. We show that the static, spherically symmetric solution found by the authors is not a solution of the assumed Weyl geometric theory with vectorial nonmetricity, but of the well-known conformally coupled scalar theory over Weyl integrable spacetime with gradient nonmetricity, instead. Besides, the solution found does not respect the gauge symmetry of the underlying theory.

##### 15.I-Love-Q in Einstein-aether Theory

**Authors:**Kai Vylet, Siddarth Ajith, Kent Yagi, Nicolás Yunes

**Abstract:** Although Lorentz symmetry is a staple of General Relativity (GR), there are several reasons to believe it may not hold in a more advanced theory of gravity, such as quantum gravity. Einstein-aether theory is a modified theory of gravity that breaks Lorentz symmetry by introducing a dynamical vector field called the aether. The theory has four coupling constants that characterize deviations from GR and that must be determined through observations. Although three of the four parameters have been constrained by various empirical observations and stability requirements, one, called $c_\omega$, remains essentially unconstrained. The aim of this work is to see if a constraint on $c_\omega$ can be derived from the I-Love-Q universal relations for neutron stars, which connect the neutron star moment of inertia (I), the tidal Love number (Love), and the quadrupole moment (Q) in a way that is insensitive to uncertainties in the neutron star equation-of-state. To understand if the theory can be constrained through such relations, we model slowly-rotating or weakly tidally-deformed neutron stars in Einstein-aether theory, derive their I-Love-Q relations, and study how they depend on $c_\omega$. We find that the I-Love-Q relations in Einstein-aether theory are insensitive to $c_\omega$ and that they are close to the relations in GR. This means that the I-Love-Q relations in Einstein-aether theory remain universal but cannot be used to constrain the theory. These results indicate that to constrain the theory with neutron stars, it is necessary to investigate relations involving other observables.

##### 1.Hamilton-Jacobi formalism for k-inflation

**Authors:**Rong-Jia Yang, Ming Liu

**Abstract:** We consider a type of k-inflation under the Hamilton-Jacobi approach. We calculate various observables such as the scalar power spectrum, the tensor-to-scalar ratio, the scalar spectra index for the case where the Hubble parameter is a power-law function of k-field. The model's parameters are constrained with Planck data and the concrete form of the potential is presented. The results show that the model can be in good agreement with observations.

##### 2.Computer Simulations of Causal Sets

**Authors:**L Glaser

**Abstract:** This review introduces Markov Chain Monte Carlo simulations in causal set theory, with a focus on the study of the 2d orders. It will first introduce the Benincasa-Dowker action on causal sets, and cover some musings on the philosophy of computer simulations. And then proceed to review results from the study of the 2d orders, first their general phase transition and scaling behavior and then results on defining a wave function of the universe using these orders and on coupling the 2d orders to an Ising like model. Including matter in this type shows a strong coupling between matter and geometry, that leads to new phase transitions. However, while the matter does induce a new phase transition, it does not change the order of the phase transition of geometry.

##### 3.Signatures of the black hole quantum atmosphere in nonlocal correlations

**Authors:**Adam Z. Kaczmarek, Dominik Szczęśniak

**Abstract:** Recently, it was suggested that the Hawking radiation may originate not at the event horizon but in the quantum region outside of it, known as the quantum atmosphere. The present study attempts to explore this argument further by assessing its role in shaping quantum correlations near a black hole. Herein, these are conveniently captured within the geometric measure of nonlocality, termed as the measurement-induced nonlocality, and found to exhibit signatures of the atmosphere. In particular, a notable loss of correlations is observed well outside the event horizon, coinciding with the peak of particles radiation in the atmosphere region. Still, the correlations are shown to be always finite therein and to continuously scale with not only the radiation temperature but also with the horizon size. Hence, some characteristics of the atmosphere appears to be detectable at the quantum correlations level, providing novel insight and means to help verify the concept of interest.

##### 4.Are multiple reflecting boundaries capable of enhancing entanglement harvesting?

**Authors:**Dipankar Barman, Bibhas Ranjan Majhi

**Abstract:** Quantum entanglement harvesting in the relativistic setup attracted a lot of attention in recent times. Acquiring more entanglement within two qubits may be very desirable to establish fruitful communication between them. On the other hand use of reflecting boundaries in a spacetime has close resemblance to the cavity quantum optomechanical systems. Here, in presence of two reflecting boundaries, we study the generation of entanglement between two uniformly accelerated Unruh- DeWitt detectors which are interacting with the background scalar fields. Like no boundary and single boundary situations, entanglement harvesting is possible for their motions in opposite Rindler wedges. We observe that the reflecting boundaries can play double roles. In some parameter space it causes suppression, while in other parameter space we can have enhancement of entanglement compared to no boundary and single boundary cases. Thus increase of boundaries has significant impact in this phenomena and a suitable choices of parameters provides diresable increment of it.

##### 5.Nonlinearities in Black Hole Ringdowns and the Quantization of Gravity

**Authors:**Thiago Guerreiro

**Abstract:** Einstein's theory of gravity admits a low energy effective quantum field description from which predictions beyond classical general relativity can be drawn. As gravitational wave detectors improve, one may ask whether non-classical features of such theory can be experimentally verified. Here we argue that nonlinear effects in black hole ringdowns can be sensitive to the graviton number statistics and other quantum properties of gravitational wave states. The prediction of ringdown signals, potentially measurable in the near future, might require the inclusion of quantum effects. This offers a new route to probing the quantum nature of gravity and gravitational wave entanglement.

##### 1.Detecting intermediate-mass black hole binaries with atom interferometer observatories: Using the resonant mode for the merger phase

**Authors:**Alejandro Torres-Orjuela

**Abstract:** Atom interferometry detectors like AION, ZAIGA, and AEDGE will be able to detect gravitational waves (GWs) at dHz covering the band between large space-based laser interferometers LISA/TianQin/Taiji and ground-based facilities LIGO/Virgo/KAGRA. They will detect the late inspiral and merger of GW sources containing intermediate-mass black holes (IMBHs) in the mass range $10^2-10^5\,{\rm M_\odot}$. We study how accurately the parameters of an IMBH binary can be measured using the noise curve of AION. Furthermore, we propose a detection scheme where the early inspiral of the binary is detected using the regular broadband mode while the merger is detected using the resonant mode. We find that by using such a detection scheme the signal-to-noise ratio (SNR) of the detection as well as the detection accuracy of the parameters can be enhanced compared to the full detection of the signal using the broadband mode. We, further, assess the impact of the necessary detection gap while switching from broadband to resonant mode studying the case of a short ($30\,{\rm s}$) and a long ($600\,{\rm s}$) gap. We find that the improvement in SNR and detection accuracy is bigger for the shorter gap but that even in the case of the long gap such a scheme can be beneficial.

##### 2.A Sensitive Test of Non-Gaussianity in Gravitational-wave Detector Data

**Authors:**Ronaldas Macas, Andrew Lundgren

**Abstract:** Methods for parameter estimation of gravitational-wave data assume that detector noise is stationary and Gaussian. Real data deviates from these assumptions, which will cause bias in the inferred parameters and incorrect estimates of the errors. We develop a sensitive test of non-Gaussianity for real gravitational-wave data which measures meaningful parameters that can be used to characterize these effects. As a test case, we investigate the quality of data cleaning performed on the binary black hole signal GW200129 which overlapped with the noise produced by the radio frequency modulation. We demonstrate that the data cleaned by LIGO-Virgo-KAGRA contains less noise than the original data, especially for frequencies below 50 Hz.

##### 3.Scalar-Induced Gravitational Waves from Ghost Inflation

**Authors:**Sebastian Garcia-Saenz, Yizhou Lu, Zhiming Shuai

**Abstract:** We calculate the scalar-induced gravitational wave energy density in the theory of Ghost Inflation, assuming scale invariance and taking into account both the power spectrum- and trispectrum-induced contributions. For the latter we consider the leading cubic and quartic couplings of the comoving curvature perturbation in addition to two parity-violating quartic operators. In the parity-even case, we find the relative importance of the trispectrum-induced signal to be suppressed by the requirement of perturbativity, strengthening a no-go theorem recently put forth. The parity-odd signal, even though also bound to be small, is non-degenerate with the Gaussian contribution and may in principle be comparable to the parity-even non-Gaussian part, thus potentially serving as a probe of the Ghost Inflation scenario and of parity violating physics during inflation.

##### 4.Competitive effects between gravitational radiation and mass variation for two-body systems in circular orbits

**Authors:**Baptiste Blachier, Aurélien Barrau, Killian Martineau, Cyril Renevey

**Abstract:** This work provides, at lower order, general analytical solutions for the orbital separation, merging time, and orbital frequency of binary systems emitting gravitational waves while being submitted to mass variations. Specific features, depending on the exponent of the mass derivative, are investigated in details. Two phenomenologically interesting cases are explicitly considered : i) binaries formed by two light primordial black holes submitted to Hawking evaporation and ii) bodies driven by a Bondi accretion of phantom dark energy. It is shown that three different regimes arise, including an intricate non-monotonic behaviour of the system. We study subtle imprints that could be associated with those phenomena. A careful analysis of the conditions of validity of the different hypotheses performed is finally carried out.

##### 5.$\mathbb{T}^{2}$- inflation: Sourced by energy-momentum squared gravity

**Authors:**Seyed Ali Hosseini Mansoori, Fereshteh Felegary, Mahmood Roshan, Ozgur Akarsu, Mohammad Sami

**Abstract:** In this paper, we examine chaotic inflation within the context of the energy-momentum squared gravity (EMSG) focusing on the energy-momentum powered gravity (EMPG) that incorporates the functional $f(\mathbb{T}^2)\propto (\mathbb{T}^2)^{\beta}$ in the Einstein-Hilbert action, in which $\beta$ is a constant and $\mathbb{T}^2\equiv T_{\mu \nu}T^{\mu \nu}$ where $T_{\mu \nu}$ is the energy-momentum tensor, which we consider to represent a single scalar field with a power-law potential. We demonstrate that the presence of EMSG terms allows the single-field monomial chaotic inflationary models to fall within current observational constraints, which are otherwise disfavored by Planck and BICEP/Keck findings. We show that the use of a non-canonical Lagrangian with chaotic potential in EMSG can lead to significantly larger values of the non-Gaussianity parameter, $f_{\rm Nl}^{\rm equi}$ whereas EMSG framework with canonical Lagrangian gives rise to results similar to those of the standard single-field model.

##### 6.Quasinormal modes and greybody factors of symmergent black hole

**Authors:**Dhruba Jyoti Gogoi, Ali Övgün, Durmuş Demir

**Abstract:** In this paper, we perform a detailed study of the quasinormal modes and greybody factors of the black holes in symmergent gravity. The relevant parameters of the symmergent gravity are the quadratic curvature term $c_{\rm O}$ and the vacuum energy parameter $\alpha$. In our analyses, effects of the both parameters are investigated. Our findings suggest that, in both positive and negative direction, large $|c_{\rm O}|$ values of the parameter on the quasinormal modes parallel the Schwarzschild black hole. Moreover, the quasinormal model spectrum is found to be sensitive to the symmergent parameter $\alpha$. We contrast the asymptotic iteration and WKB methods in regard to their predictions for the quasinormal frequencies, and find that they differ (agree) slightly at small (large) multipole moments. We analyze time-domain profiles of the perturbations, and determine the greybody factor of the symmergent black hole in the WKB regime. The symmergent parameter $\alpha$ and the quadratic curvature term $c_{\rm O}$ are shown to impact the greybody factors significantly. We provide also rigorous limits on greybody factors for scalar perturbations, and reaffirm the impact of model parameters.

##### 7.Geometry and covariance of symmetric teleparallel theories of gravity

**Authors:**Daniel Blixt, Alexey Golovnev, Maria-Jose Guzman, Ramazan Maksyutov

**Abstract:** We present the geometric foundations and derivations of equations of motion for symmetric teleparallel theories of gravity in the coincident gauge and covariant frameworks. We discuss the theoretical challenges introduced by the auxiliary fields responsible for the covariantisation procedure. We elucidate a tetradic structure interpretation behind this covariant formulation. Regarding the effect of covariantisation at the level of the equations of motion, we explicitly show that the only physical change, in case of setting an arbitrary energy-momentum tensor to the right hand side, resides in the requirement of the fulfillment of the covariant conservation laws.

##### 1.Gravitational and dark wave emission at binary merger

**Authors:**Kunio Kaneta, Kin-ya Oda, Motohiko Yoshimura

**Abstract:** The recently proposed formalism of extended Jordan-Brans-Dicke gravity makes it possible to calculate energy loss rate due to both gravitational wave and scalar field (giving the origin of dark energy) wave emission at merger of a black hole and a neutron star; a binary system of no scalar hair and a star with the scalar charge. The scalar field emission changes orbit parameters of the binary system, thereby changes detectable gravitational wave emission. When neutron stars carry significantly large scalar charge, significant dark wave (namely, scalar field wave) emission occurs at the same time of gravitational wave emission. It is found that solutions of coupled differential equations predict non-vanishing remnant dark charge after the gravitational collapse. This gives two interesting possibilities: (1) the no-hair conjecture of black hole is violated, or (2) a bosonic cloud is formed outside the event horizon of black hole. The bosonic cloud proposed in the literature is a gigantic atom made of gravitationally bound dark energy quanta surrounding a black hole. One can either constrain, or even determine, parameters of extended Jordan-Brans-Dicke gravity from accumulated gravitational wave observations of merging black hole and neutron star.

##### 2.Comment on "Gravitational Pair Production and Black Hole Evaporation"

**Authors:**Antonio Ferreiro, Jose Navarro-Salas, Silvia Pla

**Abstract:** We scrutinize the recent Letter "Gravitational pair production and black hole evaporation" by M.F. Wondrak, W.D. van Suijlekom and H. Falcke [Phys. Rev. Lett. 130, 221502 (2023); arXiv:2305.18521]. We show that some consequences based on the proposed imaginary part of the lowest order effective action are in sharp tension with exact results on pair creation in electrodynamics and cosmology. This casts serious doubt on their claims for particle production in a Schwarzschild spacetime.

##### 3.An observer's perspective of the Unruh and Hawking effects

**Authors:**Satish Ramakrishna

**Abstract:** The Unruh effect is one of the first calculations of what one would see when transiting between an inertial reference frame with its quantum field vacuum state and a non-inertial (specifically, uniformly accelerating) reference frame. The inertial reference frame's vacuum state would not correspond to the vacuum state of the non-inertial frame and the observer in that frame would see radiation, with a corresponding Bose distribution and a temperature proportional to the acceleration (in natural units). In this paper, I compute the response of this non-inertial observer to a single frequency mode in the inertial frame and deduce that, indeed, the cumulative distribution (over the observer's proper time) of frequencies observed by the accelerating observer would be the Bose distribution with a temperature proportional to the acceleration. The conclusion is that the Unruh effect (and the related Hawking effect) is generic, in that it would appear with any incoming incoherent state and the Bose distribution is obtained as a consequence of the non-inertial frame's motion, rather than some special property of the quantum vacuum.

##### 4.Stability Analysis of Cosmological models in $f(T,φ)$ Gravity

**Authors:**Amit Samaddar, S. Surendra Singh

**Abstract:** We investigated the stability condition in $f(T,\phi)$ gravity theory for considering two models by using dynamical system. We assume the forms of $G(T)$ are $(i)$ $G(T)$ = $\alpha T+\frac{\beta}{T}$, $(ii)$ $G(T)$ = $\zeta T$ ln$(\psi T)$, where $\alpha$, $\beta$, $\zeta$ and $\psi$ be the free parameters. We evaluated the equilibrium points for these models and examine the stability behavior. We found five stable critical points for Model I and three stable critical points for Model II. The phase plots for these systems are examined and discussed the physical interpretation. We illustrate all the cosmological parameters such as $\Omega_{m}$, $\Omega_{\phi}$, $q$ and $\omega_{Tot}$ at each fixed points and compare the parameters with observational values. Further, we assume hybrid scale factor and the equation of redshift and time is $t(z)=\frac{\delta}{\sigma}W\bigg[\frac{\sigma}{\delta}\bigg(\frac{1}{a_{1}(1+z)}\bigg)^{\frac{1}{\delta}}\bigg]$. We transform all the parameters in redshift by using this equation and examine the behavior of these parameters. Our models represent the accelerating stage of the Universe. The energy conditions are examined in terms of redshift and SEC is not satisfied for the model. We also find the statefinder parameters $\{r,s\}$ in terms of z and discuss the nature of $r-s$ and $r-q$ plane. For both pairs $\{r,s\}$ and $\{r,q\}$ our models represent the $\Lambda$CDM model. Hence, we determine that our $f(T,\phi)$ models are stable and it satisfies all the observational values.

##### 5.The linearized Einstein equations with sources

**Authors:**Peter Hintz

**Abstract:** On vacuum spacetimes of general dimension, we study the linearized Einstein vacuum equations with a spatially compactly supported and (necessarily) divergence-free source. We prove that the vanishing of appropriate charges of the source, defined in terms of Killing vector fields on the spacetime, is necessary and sufficient for solvability within the class of spatially compactly supported metric perturbations. The proof combines classical results by Moncrief with the solvability theory of the linearized constraint equations with control on supports developed by Corvino and Chru\'sciel-Delay.

##### 6.Gravitational quasinormal mode in internal and external region of black hole by using improved matrix method

**Authors:**Kai Lin

**Abstract:** By using Jordan decomposition, this paper improves the matrix method for solving quasinormal modes (QNMs) of black holes. As an example, the gravitational quasinormal mode (QNM) in both the internal and external regions of Schwarzschild black hole is studied. The improved matrix method avoids the need to calculate inverse matrices in the original matrix method, thereby significantly reducing the computational resources and time required to compute the coefficient square matrices of the derivatives. The research on the QNM in the internal and external regions of the Schwarzschild black hole shows that polar and axial gravitational perturbations have the same QNM frequency, but different wave functions. We compared the results of the improved matrix method with those of the Generalized Horowitz-Hubeny Method and the WKB approximation and found that the method presented in this paper has superior accuracy.

##### 7.Magnetized black holes: interplay between charge and rotation

**Authors:**Vladimir Karas, Zdenek Stuchlik

**Abstract:** Already in the cornerstone works on astrophysical black holes published as early as in 1970s, Ruffini and collaborators have revealed potential importance of an intricate interaction between the effects of strong gravitational and electromagnetic fields. Close to the event horizon of the black hole, magnetic and electric lines of force become distorted and dragged even a in purely electro-vacuum system. Moreover, as the plasma effects inevitably arise in any astrophysically realistic environment, particles of different electric charge can separate from each other, become accelerated away from the black hole or accreted onto it, and contribute to the net electric charge of the black hole. From the point of principle, the case of super-strong magnetic fields is of particular interest, as the electromagnetic field can act as a source of gravity and influence the space-time geometry. In a brief celebratory note we revisit aspects of rotation and charge within the framework of exact (asymptotically non-flat) solutions of mutually coupled Einstein-Maxwell equations that describe magnetized, rotating black holes.

##### 1.Physical Process First Law and the Entropy Change of Rindler Horizons

**Authors:**T. K. Safir, C. Fairoos, Deepak Vaid

**Abstract:** The physical process version of the first law can be obtained for bifurcate Killing horizons with certain assumptions. Especially, one has to restrict to the situations where the horizon evolution is quasi-stationary, under perturbations. We revisit the analysis of this assumption considering the horizon perturbations of Rindler horizon by a spherically symmetric object. We demonstrate that even if the quasi-stationary assumption holds, the change in entropy, in four space-time dimensions, diverges when considered between asymptotic cross-sections. However, these divergences do not appear in higher dimensions. We also analyze these features in the presence of a positive cosmological constant. In the process, we prescribe a recipe to establish the physical process first law in such ill-behaved scenarios.

##### 2.Wormhole formation in massive gravity: An analytic description

**Authors:**Ayanendu Dutta, Dhritimalya Roy, Nihal Jalal Pullisseri, Subenoy Chakraborty

**Abstract:** The present study analyses the wormhole solution both in the dRGT-$ f(R,T) $ massive gravity and Einstein massive gravity. In both the models, the anisotropic pressure solution in ultrastatic wormhole geometry gives rise to the shape function that involves massive gravity parameters $ \gamma $ and $ \Lambda $. However, the terms consisting of $ \gamma $ and $ \Lambda $ acts in such a way that the spacetime loses asymptotic flatness. Similar to the black hole solution in massive gravity, this inconsistency arises due to the repulsive effect of gravity which can be represented by the photon deflection angle that goes negative after a certain radial distance. It is investigated that the repulsive effect induced in the massive gravitons push the spacetime geometry so strongly that the asymptotic flatness is effected. On the other hand, in this model, one can have a wormhole with ordinary matter at the throat that satisfies all the energy conditions while the negative energy density is sourced by massive gravitons. Finally, using the TOV equation, it is found that the model is stable under the hydrostatic equilibrium condition.

##### 3.Constraining an Einstein-Maxwell-dilaton-axion black hole at the Galactic Center with the orbit of the S2 star

**Authors:**Rebeca Fernández Fernández, Riccardo Della Monica, Ivan de Martino

**Abstract:** We derive new constraints on the dilaton parameter appearing in the spherically-symmetric black hole solution of Einstein-Maxwell-dilaton-axion gravity, by studying the geodesic motion of the S2 star in the Galactic Center. Einstein-Maxwell-dilaton-axion black holes represent a compelling alternative to the standard black hole paradigm in General Relativity. This theory emerges from the low energy effective action of the heterotic string theory and has been proven to predict peculiar observational features from the direct imaging of black hole shadows. At a fundamental level, Einstein-Maxwell-dilaton-axion includes additional electromagnetic, dilatonic and axionic fields coupled to the space-time metric. When considering charged non-rotating black hole solutions, the additional fields endow the metric with one extra parameter $b$, called dilaton parameter, that is theoretically bound to $0<b<M$. Using publicly available astrometric data for S2 we derive an upper bound on $b\lesssim 12M$ at 95% confidence level and we demonstrate that only including the measurement of the relativistic orbital precession for S2 is sufficient to reduce this bound to $b\lesssim 1.4M$ at the same confidence level. Additionally, using a mock data mimicking future observations of S2 with the GRAVITY interferometer, we show that improved astrometric precision can help further narrow down the allowed dilaton parameter range to $b\lesssim0.033M$ after monitoring the S2 orbit for one and a half period.

##### 4.MultiCarroll dynamics

**Authors:**P. -M. Zhang, H-X. Zeng, P. A. Horvathy

**Abstract:** While a single Carroll particle can not move, a multiparticle system with momentum-dependent interaction \underline{can}: the center-of-mass is fixed however relative motion is possible, confirming a previous statement made by Bergshoeff et al \cite{Bergshoeff14}. Analogous results are obtained for electric dipoles with the roles of the center-of-mass and the relative position interchanged. Immobility can also be deduced from the Carroll boost symmetry.

##### 5.On the physical viability of black hole solutions in Einsteinian Cubic Gravity and its generalisations

**Authors:**Jose Beltrán Jiménez, Alejandro Jiménez-Cano

**Abstract:** In this note, we discuss the pathological nature of black holes in Einsteinian Cubic gravity and its extensions. We compute the equations for the odd perturbations and show how spherically symmetric solutions that asymptotically approach a maximally symmetric space (Minkowski, de Sitter or anti-de Sitter) are associated to having an asymptotically degenerate principal part of the equations. We use these results to argue that the encountered problems will be generic for any other cubic or higher-order with a reduced linear spectrum around maximally symmetric spaces except the well-known healthy case of $f(R)$. We highlight that these pathologies are only alarming when the theory is regarded as a complete theory, but not when considered as a perturbative correction to GR (as in e.g. the effective field theory framework) since the the low-energy physics remains safe from them. Our results thus cast doubts on possible resolutions of the singularities or non-perturbative effects on horizons based on these theories.

##### 6.Vacuum polarisation and regular gravitational collapse

**Authors:**Valentin Boyanov

**Abstract:** It is the goal of this thesis to revisit and revise the problem of black hole formation and evolution in semiclassical gravity -- a theory in which spacetime is treated classically, while matter admits a quantum description, coupling to gravity through an expectation value of a stress-energy tensor operator. We examine the vacuum expectation value of this operator in a variety of spacetimes in which trapped regions form or are close to forming, drawing conclusions regarding the semiclassical dynamics of spacetime in these scenarios.

##### 7.When to Point Your Telescopes: Gravitational Wave Trigger Classification for Real-Time Multi-Messenger Followup Observations

**Authors:**Anarya Ray, Wanting Niu, Shio Sakon, Becca Ewing, Jolien D. E. Creighton, Chad Hanna, Shomik Adhicary, Pratyusava Baral, Amanda Baylor, Kipp Cannon, Sarah Caudill, Bryce Cousins, Heather Fong, Richard N. George, Patrick Godwin, Reiko Harada, Yun-Jing Huang, Rachael Huxford, Prathamesh Joshi, Shasvath Kapadia, James Kennington, Soichiro Kuwahara, Alvin K. Y. Li, Ryan Magee, Duncan Meacher, Cody Messick, Soichiro Morisaki, Debnandini Mukherjee, Alex Pace, Cort Posnansky, Surabhi Sachdev, Divya Singh, Ron Tapia, Leo Tsukada, Takuya Tsutsui, Koh Ueno, Aaron Viets, Leslie Wade, Madeline Wade

**Abstract:** We develop a robust and self-consistent framework to extract and classify gravitational wave candidates from noisy data, for the purpose of assisting in real-time multi-messenger follow-ups during LIGO-Virgo-KAGRA's fourth observing run~(O4). Our formalism implements several improvements to the low latency calculation of the probability of astrophysical origin~(\PASTRO{}), so as to correctly account for various factors such as the sensitivity change between observing runs, and the deviation of the recovered template waveform from the true gravitational wave signal that can strongly bias said calculation. We demonstrate the high accuracy with which our new formalism recovers and classifies gravitational wave triggers, by analyzing replay data from previous observing runs injected with simulated sources of different categories. We show that these improvements enable the correct identification of the majority of simulated sources, many of which would have otherwise been misclassified. We carry out the aforementioned analysis by implementing our formalism through the \GSTLAL{} search pipeline even though it can be used in conjunction with potentially any matched filtering pipeline. Armed with robust and self-consistent \PASTRO{} values, the \GSTLAL{} pipeline can be expected to provide accurate source classification information for assisting in multi-messenger follow-up observations to gravitational wave alerts sent out during O4.

##### 8.Analysis of a regular black hole in Verlinde's gravity

**Authors:**A. A. Araújo Filho

**Abstract:** This work focuses on the examination of a regular black hole within Verlinde's emergent gravity, specifically investigating the Hayward--like (modified) solution. The study reveals the existence of a single event horizon under certain conditions. Our results indicate phase transitions and forbidden regions based on the analysis of heat capacity and \textit{Hawking} temperature. Geodesic trajectories and critical orbits (photon spheres) are calculated, highlighting the presence of outer and inner light rings. Additionally, we investigate the black hole shadows. Furthermore, the \textit{quasinormal} modes are explored using third-- and sixth--order WKB approximations. In particular, we observe stable and unstable oscillations for certain frequencies. Finally, in order to comprehend the phenomena of time--dependent scattering in this scenario, we provide an investigation of the time--domain solution.

##### 1.The covariant approach to static spacetimes in Einstein and extended gravity theories

**Authors:**Carlo Alberto Mantica, Luca Guido Molinari

**Abstract:** We present a covariant study of static space-times, as such and as solutions of gravity theories. By expressing the relevant tensors through the velocity and the acceleration vectors that characterise static space-times, the field equations provide a natural non-redundant set of scalar equations. The same vectors suggest the form of a Faraday tensor, that is studied in itself and in (non)-linear electrodynamics. In spherical symmetry, we evaluate the explicit expressions of the Ricci, the Weyl, the Cotton and the Bach tensors. Simple restrictions on the coefficients yield well known and new solutions in Einstein, f(R), Cotton and Conformal gravity, with or without charges, in vacuo or with fluid source.

##### 2.Tunneling Newtonian Universe

**Authors:**Eugene B. Kolomeisky

**Abstract:** We analyze quantum-mechanical counterpart of Newtonian cosmology and show that effects of zero-point motion eliminate classical density singularity. Quantum effects are particularly significant for closed Universes where without the cosmological constant the energy spectrum and space curvature are quantized. When small positive cosmological constant is included, these states become quasi-stationary and decay via tunneling. Corresponding metastable Universes evolve in three stages: long period of gestation followed by rapid tunneling expansion further followed by slower Hubble expansion.

##### 3.Lorentzian quantum cosmology from effective spin foams

**Authors:**Bianca Dittrich, José Padua-Argüelles

**Abstract:** Effective spin foams provide the computationally most efficient spin foam models yet and are therefore ideally suited for applications e.g. to quantum cosmology. We provide here the first effective spin foam computations of a finite time evolution step in a Lorentzian quantum de Sitter universe. We will consider a set-up which computes the no-boundary wave function, as well as a set-up describing the transition between two finite scale factors. A key property of spin foams is that they implement discrete spectra for the areas. We therefore study the effects that are induced by the discrete spectra. To perform these computations we had to identify a technique to deal with highly oscillating and slowly converging, or even diverging sums. We illustrate here that high order Shanks transformation work very well and are a promising tool for the evaluation of Lorentzian (gravitational) path integrals and spin foam sums.

##### 4.Extended phase space quantization of a black hole interior model in Loop Quantum Cosmology

**Authors:**Beatriz Elizaga Navascués, Guillermo A. Mena Marugán, Andrés Mínguez Sánchez

**Abstract:** Considerable attention has been paid to the study of the quantum geometry of nonrotating black holes within the framework of Loop Quantum Cosmology. This interest has been reinvigorated since the introduction of a novel effective model by Ashtekar, Olmedo and Singh. Despite recent advances in its foundation, there are certain questions about its quantization that still remain open. Here we complete this quantization taking as starting point an extended phase space formalism suggested by several authors, including the proposers of the model. Adopting a prescription that has proven succesful in Loop Quantum Cosmology, we construct an operator representation of the Hamiltonian constraint. By searching for solutions to this constraint operator in a sufficiently large set of dual states, we show that it can be solved for a continuous range of the black hole mass. This fact seems in favour of a conventional classical limit (at least for large masses) and contrasts with recent works that advocate a discrete spectrum. We present an algorithm that determines the solutions in closed form. To build the corresponding physical Hilbert space and conclude the quantization, we carry out an asymptotic analysis of those solutions, which allows us to introduce a suitable inner product on them.

##### 1.Quantum-spacetime effects on nonrelativistic Schrödinger evolution

**Authors:**Fabian Wagner, Gislaine Varão, Iarley P. Lobo, Valdir B. Bezerra

**Abstract:** The last three decades have witnessed the surge of quantum gravity phenomenology in the ultraviolet regime as exemplified by the Planck-scale accuracy of time-delay measurements from highly energetic astrophysical events. Yet, recent advances in precision measurements and control over quantum phenomena may usher in a new era of low-energy quantum gravity phenomenology. In this study, we investigate relativistic modified dispersion relations (MDRs) in curved spacetime and derive the corresponding nonrelativistic Schr\"odinger equation using two complementary approaches. First, we take the nonrelativistic limit, and canonically quantise the result. Second, we apply a WKB-like expansion to an MDR-inspired deformed relativistic wave equation. Within the area of applicability of single-particle quantum mechanics, both approaches imply equivalent results. Surprisingly, we recognise in the generalized uncertainty principle (GUP), the prevailing approach in nonrelativistic quantum gravity phenomenology, the MDR which is least amenable to low-energy experiments. Consequently, importing data from the mentioned time-delay measurements, we constrain the linear GUP up to the Planck scale and improve on current bounds to the quadratic one by 17 orders of magnitude. MDRs with larger implications in the infrared, however, can be tightly constrained in the nonrelativistic regime. We use the ensuing deviation from the equivalence principle to bound some MDRs, for example the one customarily associated with the bicrossproduct basis of the $\kappa$-Poincar\'e algebra, to up to four orders of magnitude below the Planck scale.

##### 2.Time-domain supersymmetry for massless scalar and electromagnetic fields in anisotropic cosmologies

**Authors:**Felipe A. Asenjo, Sergio A. Hojman

**Abstract:** It is shown that any cosmological anisotropic model produces supersymmetric theories for both massless scalar and electromagnetic fields. This supersymmetric theory is the time-domain analogue of a supersymmetric quantum mechanical theory. In this case, the variations of the anisotropic scale factors of the Universe are responsible for triggering the supersymmetry. For scalar fields, the superpartner fields evolve in two different cosmological scenarios (Universes). On the other hand, for propagating electromagnetic fields, supersymmetry is manifested through its polarization degrees of freedom in one Universe. In this case, polarization degrees of freedom of electromagnetic waves, which are orthogonal to its propagation direction, become superpartners from each other. This behavior can be measured, for example, through the rotation of the plane of polarization of cosmological light.

##### 3.Hawking radiation from an analogue bouncing geometry

**Authors:**Alberto García Martín-Caro, Gerardo García-Moreno, Javier Olmedo, Jose M. Sánchez Velázquez

**Abstract:** We propose a setting that simulates Hawking radiation from an analogue bouncing geometry, i.e., a collapsing geometry that reverts its collapse after a finite time, in a setup consisting of a coplanar waveguide terminated in superconducting quantum-interference devices at both ends. We demonstrate experimental feasibility of the proposed setup within the current technology. Our analysis illustrates the resilience of Hawking radiation under changes in the physics at energy scales much larger than the temperature, supporting the idea that regular alternatives to black holes would also emit Hawking radiation.

##### 4.Thermodynamics and weak cosmic censorship conjecture for a Kerr-Newman Taub-NUT black hole

**Authors:**Si-Jiang Yang, Wen-Di Guo, Shao-Wen Wei, Yu-Xiao Liu

**Abstract:** Stimulated by the recent researches of black hole thermodynamics for black hole with Newman-Unti-Tamburino (NUT) parameter, we investigate the thermodynamics and weak cosmic censorship conjecture for a Kerr-Newman Taub-NUT black hole. By defining the electric charge as a Komar integral over the event horizon, we construct a consistent first law of black hole thermodynamics for a Kerr-Newman Taub-NUT black hole through Euclidean action. Having the first law of black hole thermodynamics, we investigate the weak cosmic censorship conjecture for the black hole with a charged test particle and a complex scalar field. We find that an extremal black hole cannot be destroyed by a charged test particle and a complex scalar field. For a near-extremal black hole with small NUT parameter, it can be destroyed by a charged test particle but cannot be destroyed by a complex scalar field. Since there are many different viewpoints on thermodynamics for black holes with NUT parameter, the investigation of weak cosmic censorship conjecture might provide a preliminary selection for the thermodynamics for black holes with NUT parameter.

##### 5.Weakly Lensed Gravitational Waves: Probing Cosmic Structures with Wave-Optics Features

**Authors:**Stefano Savastano, Giovanni Tambalo, Hector Villarrubia-Rojo, Miguel Zumalacarregui

**Abstract:** Every signal propagating through the universe is at least weakly lensed by the intervening gravitational field. In some situations, wave-optics phenomena (diffraction, interference) can be observed as frequency-dependent modulations of the waveform of gravitational waves (GWs). We will denote these signatures as Wave-Optics Features (WOFs) and analyze them in detail. Our framework can efficiently and accurately compute WOF in the single-image regime, of which weak lensing is a limit. The phenomenology of WOF is rich and offers valuable information: the dense cusps of individual halos appear as peaks in Green's function for lensing. If resolved, these features probe the number, effective masses, spatial distribution and inner profiles of substructures. High signal-to-noise GW signals reveal WOFs well beyond the Einstein radius, leading to a fair probability of observation by upcoming detectors such as LISA. Potential applications of WOF include reconstruction of the lens' projected density, delensing standard sirens and inferring large-scale structure morphology and the halo mass function. Because WOF are sourced by light halos with negligible baryonic content, their detection (or lack thereof) holds promise to test dark matter scenarios.

##### 6.Series Solution for Interaction of Scalar Plane Wave with Spatially Decaying Gravitational Wave

**Authors:**Jesse Elder, Todd Fugleberg

**Abstract:** In this paper we present the power series solution of the Klein-Gordon equation in the spacetime background of a gravitational wave with amplitude that decays with distance from the source. The resulting solution describes the interaction of a scalar plane wave travelling in an arbitrary direction relative to the direction of propagation of the gravitational wave. This solution has the unexpected property that as the scalar wave approaches collinearity with the gravitational wave there is a rapid transition in the form of the solution. The solution in the collinear limit exhibits a resonance phenomenon which distinguishes these results from previous analyses involving plane gravitational wave backgrounds. We discuss in detail the similarities and differences between the solutions for plane gravitational waves and gravitational waves with amplitude that decreases with distance from the source. We give an argument that this solution of the Klein-Gordon equation only describes the interaction of a gravitational wave with a scalar wave and that the gravitational wave will not produce a scalar waveform in a vacuum. The interaction between the gravitational and scalar waves lead to both sinusoidal time-dependent fluctuations in, and time-independent enhancement of, the scalar current in the direction of the gravitational wave. Finally, we discuss the possibility of observable effects of this interaction.

##### 1.From entropy to gravitational entropy

**Authors:**Sarbari Guha

**Abstract:** The concept of entropy forms the backbone of the principles of thermodynamics. R.C. Tolman initiated a correlation between gravity and thermodynamics. The development of black hole thermodynamics and the generalized second law of thermodynamics led to Penrose's conjecture that the Weyl tensor should serve as a measure of the entropy of the free gravitational field. This entropy reflects the degrees of freedom associated with the free gravitational field. The proposition of gravitational entropy justifies the initial entropy of the universe. This entropy function had to be associated with the dynamics of the free gravitational field from the time of the big bang, so that a gravity-dominated evolution of the universe preserves the second law of thermodynamics. Moreover, the concept of black hole entropy emerges as a particular case of the entropy of the free gravitational field. However, a self-consistent notion of gravitational entropy in the context of cosmological structure formation has eluded us till today. Various proposals have been put forward, initially based on Penrose's Weyl Curvature Hypothesis, and subsequently modified to fit the needs of specific geometries and matter distributions. Such proposals were basically geometric in nature. A few years back a new definition of gravitational entropy was proposed from the considerations of the relativistic Gibb's equation and based on the square root of the Bel-Robinson tensor, the simplest divergence-free tensor derived from the Weyl tensor. Even this proposal is valid only for a restricted class of spacetimes. A complete self-consistent description of gravitational entropy encompassing black hole physics and cosmological dynamics is yet to emerge. In this article, we gather an overview of the concept of gravitational entropy, following it up with the development of the various proposals of gravitational entropy.

##### 2.Cosmological perturbations out of the box I

**Authors:**Emine Şeyma Kutluk

**Abstract:** Using the tool of Hodge-Morrey decomposition of forms, we prove a new decomposition of symmetric rank-2 tensors on flat manifolds with boundary. Using this we reconstruct a new cosmological perturbation theory that allows for the scalar-vector-tensor type separation of the linearized Einstein equations with general boundary conditions. We discuss gauge transformations, gauge invariant quantities and as an example how the new decomposition works out in the single-field inflation scenario. For the scalar modes we get two copies of Mukhanov-Sasaki equation, one of them with a slight modification. Additionally we run a Weinberg-like argument for the existence adiabatic modes, and find some gauge-invariant solutions to the perturbations that exists whatever the constituents of the universe are.

##### 3.A general method for solving light-like geodesics

**Authors:**Ren-Qi Pan, Xi He

**Abstract:** A universal method to solve the differential equations of light-like geodesics is developed. The validity of this method depends on a new theorem, which is introduced for light-like geodesics in analogy to Beltrami's "geometrical" method for time-like geodesics. we apply the method to the Schwarzschild and Kerr spacetime as two examples. The general solutions of the light-like geodesic equations in the two spacetimes are derived straightforwadly. After setting $\theta=\pi/2$, the general light-like geodesics in Schwarzschild spacetime reduce to the same expression as that in literatures. The method developed and results obtained in this paper may be useful in modeling dynamical phenomena in strong gravitaional fields like black holes since the solutions are expressed in terms of elliptic integrals, which can be calculated effectively.

##### 4.Regular black hole from regular initial data

**Authors:**Karim Mosani, Pankaj S. Joshi

**Abstract:** Recently there has been an interest in exploring black holes that are regular in that the central curvature singularity is avoided. Here, we give a recipe to obtain a regular black hole spacetime from the unhindered gravitational collapse from regular initial data of a spherically symmetric perfect fluid. While the classic Oppenheimer-Snyder collapse model necessarily produces a black hole with a Schwarzschild singularity at the centre, we show here that there are classes of regular initial conditions when collapse gives rise to a regular black hole.