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

##### 1.Loss of hyperbolicity and tachyons in generalized Proca theories

**Authors:**Kıvanç İ. Ünlütürk, Andrew Coates, Fethi M. Ramazanoğlu

**Abstract:** Various groups recently demonstrated that the time evolution of simplest self-interacting vector fields, those with self-interaction potentials, can break down after a finite duration in what is called loss of hyperbolicity. We establish that this is not an isolated issue, and other generalizations of the Proca theory suffer from the same problem. Specifically, we show that vector field theories with derivative self-interactions have a similar pathology. For this, we derive the effective metric that governs the dynamics, and show that it can change signature during time evolution. We also show that, generalized Proca theories may suffer from tachyonic instabilities as well, which lead to another form of unphysical behavior.

##### 2.Gravito-electromagnetic perturbations of MOG black holes with a cosmological constant: Quasinormal modes and Ringdown waveforms

**Authors:**Wentao Liu, Xiongjun Fang, Jiliang Jing, Jieci Wang

**Abstract:** In this paper, we present black hole solutions with a cosmological constant in the MOG theory, where the strength of the gravitational constant is determined by $G = G_\text{N}(1+\alpha)$. We derive the master equations for gravito-electromagnetic perturbations and numerically solve for the Quasinormal Mode (QNM) spectrum and the ringdown waveforms. Our results show that increasing either the MOG parameter $\alpha$ or the cosmological constant $\Lambda$ leads to a decrease in both the real and imaginary parts of the QNM frequencies for electromagnetic and gravitational modes, compared to standard Schwarzschild-de Sitter (S-dS) or MOG black holes, respectively. Meanwhile, the result indicates that in the MOG-de Sitter spacetime, the frequencies for electromagnetic and gravitational modes display strict isospectrality, and exhibit the same ringdown waveforms. Our findings have implications for the ringdown phase of mergers involving massive compact objects, which is of particular relevance given the recent detections of gravitational waves by LIGO.

##### 3.Spinning Black Holes with Axion Hair

**Authors:**Clare Burrage, Pedro G. S. Fernandes, Richard Brito, Vitor Cardoso

**Abstract:** In this work we construct and analyse non-perturbative stationary and axially-symmetric black hole solutions in General Relativity coupled to an electromagnetic and an axion field. The axion field is coupled to the electromagnetic field, which leads to hairy solutions in the presence of an electric charge and rotation. We investigate the existence and characteristics of these solutions for different values of the spin, charge and coupling constant. Our analysis shows the presence of violations of the Kerr-Newman bound, solutions with large positive and negative values of the gyromagnetic ratio, and the existence of multiple branches of solutions with distinct properties, demonstrating that black hole uniqueness does not hold in this scenario. The code used in this study is publicly available, providing a valuable tool for further research on this model.

##### 4.Tetrad Fields, Reference Frames, and the Gravitational Energy-Momentum in the Teleparallel Equivalent of General Relativity

**Authors:**J. W. Maluf, F. L. Carneiro, S. C. Ulhoa, J. F. da Rocha-Neto

**Abstract:** We review the concept and definitions of the energy-momentum and angular momentum of the gravitational field in the teleparallel equivalent of general relativity (TEGR). The importance of these definitions is justified by three major reasons. First, the TEGR is a well established and widely accepted formulation of the gravitational field, whose basic field strength is the torsion tensor of the Weitzenb\"ock connection. Second, in the phase space of the TEGR there exists an algebra of the Poincar\'e group. Not only the definitions of the gravitational energy-momentum and 4-angular momentum satisfy this algebra, but also the first class constraints related to these definitions satisfy the algebra. And third, innumerous applications of these definitions lead to physically consistent results. These definitions follow from a well established Hamiltonian formulation, and rely on the idea of localization of the gravitational energy. In this review we revisit the concept of localizability of the gravitational energy, in light of results obtained in recent years. We have studied the behaviour of free particles in the space-time of plane fronted gravitational waves (pp-waves). Free particles are here understood as particles that are not subject to external forces other than the gravitational acceleration due to pp-waves. Since these particles acquire or loose kinetic energy locally, the transfer of energy from or to the gravitational field must also be localized. We consider this theoretical result an important and definite argument in favour of the localization of the gravitational energy-momentum, and by extension, of the gravitational 4-angular momentum.

##### 5.Does the metric play a fundamental role in the building of gravitational models?

**Authors:**Oscar Castillo-Felisola, Jose Perdiguero

**Abstract:** The idea that General Relativity could be an effective model, of a yet unknown theory of gravity, has gained momentum among theoretical physicists. The polynomial affine model of gravity is an alternative model of affine gravity that possesses many desirable features to pursue a quantum theory of gravitation. In this paper we argue that such features are a consequence of the lack of a metric structure in the building of the model, even though a emergent metric could be defined. The model introduces additional degrees of freedom associated to the geometric properties of the space, which might shed light to understand the nature of the dark sector of the Universe. When the model is coupled to a scalar field, it is possible to define inflationary scenarios.

##### 6.Gravity-induced electric currents

**Authors:**David Edward Bruschi

**Abstract:** We study the generation of an electric current in an ideal conducting coil, immersed in a magnetic field, due to the occurrence of a gravitational perturbation. We show that this effect can be used to detect gravitational waves impinging on the coil as well as gravitational gradients when the coil moves in a static background gravitational field. Our work opens the way to employing induced electric signals to detect dynamical gravitational fields and for gradiometry.

##### 7.Macroscopic noncommutative-geometry wormholes as emergent phenomena

**Authors:**Peter K. F. Kuhfittig

**Abstract:** Noncommutative geometry, an offshoot of string theory, replaces point-like particles by smeared objects. These local effects have led to wormhole solutions in a semiclassical setting, but it has also been claimed that the noncommutative effects can be implemented by modifying only the energy momentum tensor in the Einstein field equations, while leaving the Einstein tensor unchanged. The implication is that noncommutative-geometry wormholes could be macroscopic. The purpose of this paper is to confirm this conclusion in a simpler and more concrete manner by showing that the throat radius can indeed be macroscopic. This result can be readily explained by considering the noncommutative-geometry background to be a fundamental property and the macroscopic wormhole spacetime to be emergent.

##### 8.A Survey of Gravitational Waves

**Authors:**Frans Pretorius

**Abstract:** We review the state of the field of gravitational wave astrophysics, framing the challenges, current observations, and future prospects within the context of the predictions of Einstein's theory of general relativity.

##### 9.Thick fluid disks around binary black holes

**Authors:**S. V. Chernov

**Abstract:** A model of a thick fluid disk around a binary black hole is considered. A binary black hole is described by the Majumdar-Papapetrou solution. The hydrodynamic equations in this metric are written out. Exact analytical solutions are presented. Generalization to the case of a toroidal magnetic field is carried out.

##### 10.Follow-up analyses to the O3 LIGO-Virgo-KAGRA lensing searches

**Authors:**Justin Janquart, Mick Wright, Srashti Goyal, Juno C. L. Chan, Apratim Ganguly, Ángel Garrón, David Keitel, Alvin K. Y. Li, Anna Liu, Rico K. L. Lo, Anuj Mishra, Anupreeta More, Hemantakumar Phurailatpam, Prasia Pankunni, Sylvia Biscoveanu, Pablo Cremonese, Jean-René Cudell, José M. Ezquiaga, Juan Garcia-Bellido, Otto A. Hannuksela, K. Haris, Ian Harry, Martin Hendry, Sascha Husa, Shasvath Kapadia, Tjonnie G. F. Li, Ignacio Magaña Hernandez, Suvodip Mukherjee, Eungwang Seo, Chris Van Den Broek, John Veitch

**Abstract:** Along their path from source to observer, gravitational waves may be gravitationally lensed by massive objects. This results in distortions of the observed signal which can be used to extract new information about fundamental physics, astrophysics, and cosmology. Searches for these distortions amongst the observed signals from the current detector network have already been carried out, though there have as yet been no confident detections. However, predictions of the observation rate of lensing suggest detection in the future is a realistic possibility. Therefore, preparations need to be made to thoroughly investigate the candidate lensed signals. In this work, we present some of the follow-up analyses and strategies that could be applied to assess the significance of such events and ascertain what information may be extracted about the lens-source system from such candidate signals by applying them to a number of O3 candidate events, even if these signals did not yield a high significance for any of the lensing hypotheses. For strongly-lensed candidates, we verify their significance using a background of simulated unlensed events and statistics computed from lensing catalogs. We also look for potential electromagnetic counterparts. In addition, we analyse in detail a candidate for a strongly-lensed sub-threshold counterpart that is identified by a new method. For microlensing candidates, we perform model selection using a number of lens models to investigate our ability to determine the mass density profile of the lens and constrain the lens parameters. We also look for millilensing signatures in one of the lensed candidates. Applying these additional analyses does not lead to any additional evidence for lensing in the candidates that have been examined. However, it does provide important insight into potential avenues to deal with high-significance candidates in future observations.

##### 11.Dynamical analysis in Chameleon dark energy

**Authors:**Andronikos Paliathanasis

**Abstract:** We present a detailed analysis of the phase-space for the field equations in scalar field cosmology with a chameleon cosmology in a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker spacetime. For the matter source we assume that it is an ideal gas with a constant equation of state parameter, while for the scalar field potential and the coupling function of the chameleon mechanism we consider four different sets which provide four different models. We consider the $H$-normalization approach and we write the field equations with the help of dimensionless variables. The asymptotic solutions are determined from where we find that the theory can describe the main eras of cosmological history and evolution. Future attractors which describe acceleration exist, however we found past acceleration solutions related to the inflationary era, as also the radiation epoch and the matter dominated eras are provided by the dynamics. We conclude that the Chameleon dark energy model can be used as a unified model for the elements which contribute to the dark sector of the universe.

##### 1.Growth rate of spherical voids with non-comoving Dark Matter and Baryons

**Authors:**Fernando A. Pizaña, Juan Carlos Hidalgo, Ismael Delgado Gaspar, Roberto A. Sussman

**Abstract:** We present numerical solutions to Einstein's equations describing large spherical cosmic voids constituted by two components; dark matter and baryons, with a non-vanishing initial relative velocity, in an asymptotically homogeneous background compatible with the $\Lambda$CDM concordance model. We compute numerically the evolution of such configurations in the dark matter frame, with a hypothetical homogeneous distribution of baryons, but respecting the values dictated by the concordance model for the average baryon-to-dark matter density ratio. We reproduce the well known formation of overdensities at the edge of the void, and recover the Lemaitre-Tolman-Bondi solutions in the comoving limit of our simulations. We compute the average growth factor of matter fluctuations, and find that it departs significantly from the linear perturbative prescription even in the comoving case, where the non-linearity of inhomogeneities has an impact.

##### 2.Gravitational waves from extreme mass ratio inspirals around a hairy Kerr black hole

**Authors:**Tieguang Zi, Peng-Cheng Li

**Abstract:** Recently, Contreras et al. \cite{Contreras:2021yxe} introduced a new type of black hole, called hairy Kerr black hole (HKBH), which describes a Kerr BH surrounded by an axially symmetric fluid with conserved energy momentum tensor. In this paper, we compute the gravitational waves emitted from the extreme mass ratio inspirals around the HKBHs. We solve the Dudley-Finley equation, which describes the gravitational perturbations of the HKBH, and obtain the energy fluxes induced by a stellar-mass compact object moving on the equatorial, circular orbits. Using the adiabatic approximation, we evolved the radii of the circular orbits by taking into account the backreaction of gravitational radiation. Then we calculate the dephasing and mismatch of the EMRI waveforms from the HKBH and Kerr BH to assess the difference between them. The results demonstrate that the EMRI waveforms from the HKBH with deviation parameter larger than $0.001$ and hair charge smaller than $1.5M$ can be discerned by LISA.

##### 3.Thermality of the zero-point length and gravitational selfduality

**Authors:**P. Fernandez de Cordoba, J. M. Isidro, Rudranil Roy

**Abstract:** It has been argued that the existence of a zero-point length is the hallmark of quantum gravity. In this letter we suggest a thermal mechanism whereby this quantum of length arises in flat, Euclidean spacetime $\mathbb{R}^d$. For this we consider the infinite sequence of all flat, Euclidean spacetimes $\mathbb{R}^{d'}$ with $d'\geq d$, and postulate a probability distribution for each $d'$ to occur. The distribution considered is that of a canonical ensemble at temperature $T$, the energy levels those of a 1-dimensional harmonic oscillator. Since both the harmonic energy levels and the spacetime dimensions are evenly spaced, one can identify the canonical distribution of harmonic-oscillator eigenvalues with that of dimensions $d'$. The state describing this statistical ensemble has a mean square deviation in the position operator, that can be interpreted as a quantum of length. Thus placing an oscillator in thermal equilibrium with a bath provides a thermal mechanism whereby a zero-point length is generated. The quantum-gravitational implications of this construction are then discussed. In particular, a model is presented that realises a conjectured duality between a weakly gravitational, strongly quantum system and a weakly quantum, strongly gravitational system.

##### 4.Spin network Entanglement and Bulk-Boundary Map in Loop Quantum Gravity

**Authors:**Qian Chen

**Abstract:** This thesis is dedicated to the study of open spin networks. We formulate quasi-local descriptions of loop quantum gravity. We investigate the coarse-graining procedure via tracing over bulk degrees of freedom, which encodes all that we can know about the quantum state of geometry from probing the boundary. We prove a boundary-to bulk universal reconstruction procedure, to be understood as a purification of the mixed boundary state into a pure bulk state. We then move to define multipartite entanglement in spin networks, and show the computation of entanglement excitation from holonomy operator, which also allows us to glimpse bulk curvature from entanglement. Moreover, by investigating another coarse-graining procedure - via gauge-fixing, which does not trace over any bulk degrees of freedom, we show a new interesting connection between bulk geometry and boundary observables via the dynamics of entanglement. Finally, we define the spin network entanglement between spin sub-networks, which correspond to spatial sub-regions. We then generalize the coarse-graining approach, and prove that the entanglement between spin sub-networks is preserved under the coarse-graining (via gauge-fixing).

##### 5.Joule-Thomson expansion and Optical behaviour of Reissner-Nordström-Anti-de Sitter black holes in Rastall gravity surrounded by a Quintessence field

**Authors:**Dhruba Jyoti Gogoi, Yassine Sekhmani, Digbijay Kalita, Naba Jyoti Gogoi, Jyatsnasree Bora

**Abstract:** This paper deals with the thermodynamics, Joule-Thomson expansion and optical behaviour of a Reissner-Nordstr\"om-anti-de Sitter black hole in Rastall gravity surrounded by a quintessence field. The black hole solution obtained in this framework is different from a corresponding black hole in General Relativity. The black hole metric function, as well as the Hawking temperature, is affected by the presence of energy-momentum conservation violation. The presence of energy-momentum conservation violation also affects the isenthalpic and inversion temperature curves, and with an increase in the Rastall parameter, the inversion temperature rises slowly. The impacts of other parameters, such as charge, structural constant etc., are investigated and compared. The black hole shadow, as well as the energy emission rate of the black hole, decreases with an increase in the Rastall parameter. Hence, the black holes evaporate slowly in presence of energy-momentum conservation violation.

##### 6.Electromagnetic Quasinormal modes of Dyonic AdS black holes with quasi-topological electromagnetism in a Horndeski gravity theory mimicking EGB gravity at $D \rightarrow 4$

**Authors:**Yassine Sekhmani, Dhruba Jyoti Gogoi

**Abstract:** We investigate some properties of a black hole in a Horndeski gravity theory mimicking Einstein-Gauss-Bonnet (EGB) gravity at $D \rightarrow 4$. Borrowing ideas from quasitopological gravities provide a matter source of dyonic fields, in which the black hole solution carries two charges, electric and magnetic, in the context of the EGB gravity. However, due to several limitations of the EGB gravity in $D \rightarrow 4$, we consider a Horndeski gravity theory which can mimic EGB gravity in $D \rightarrow 4$. The essential practice used in this paper is the electromagnetic quasinormal modes process, with the goal of discovering the spectrum of such an electromagnetic perturbation over the black hole spacetime. The Wentzel-Kramer-Brillouin (WKB) approximation is used to achieve the desired results. The study shows that both the charges have similar impacts on the quasinormal modes.

##### 7.Gauge fields through the Big Bang

**Authors:**Martina Adamo, Flavio Mercati

**Abstract:** Recent studies have demonstrated the possibility to uphold classical determinism within gravitational singularities, showcasing the ability to uniquely extend Einstein's equations across the singularity in certain symmetry-reduced models. This extension can be achieved by allowing the orientation of spatial hypersurfaces to dynamically change. Furthermore, a crucial aspect of the analysis revolves around the formulation of the dynamical equations in terms of physical degrees of freedom, demonstrating their regularity at the singularity. Remarkably, singular behavior is found to be confined solely to the gauge/unphysical degrees of freedom. This paper extends these results to gravity coupled with Abelian and non-Abelian gauge fields in a symmetry-reduced model (homogeneous anisotropic universe). Near the Big Bang, the dynamics of the geometry and the gauge fields is reformulated in a way that shows that determinism is preserved, assuming a change in orientation at the singularity. The gauge fields are demonstrated to maintain their orientation throughout the singularity, indicating that the predicted orientation change of spatial hypersurfaces holds physical significance. This observation suggests that an observer can discern the specific side of the Big Bang they inhabit.

##### 8.On Thermodynamics of Kerr Black Hole

**Authors:**S. C. Ulhoa, A. F. Santos, E. P. Spaniol, Faqir C. Khanna

**Abstract:** The gravitational Stefan-Boltzmann law is considered for the Kerr black hole in the weak-field limit. The energy-momentum tensor predicted by Teleparallelism Equivalent to General Relativity (TEGR) is used in the Thermo Field Dynamics (TFD) formalism to thermalize the field. A temperature-dependent gravitational pressure is obtained. Regions of divergent heat capacity are observed. According to Landau theory, it allows the existence of distinct phases around the Kerr black hole.

##### 9.Constraining quantum fluctuations of spacetime foam from BBN

**Authors:**Saurya Das, Gaetano Lambiase, Elias C. Vagenas

**Abstract:** A possibility to describe quantum gravitational fluctuations of the spacetime background is provided by virtual $D$-branes. These effects may induce a tiny violation of the Lorentz invariance (as well as a possible violation of the equivalence principle). In this framework, we study the formation of light elements in the early Universe (Big Bang Nucleosynthesis). By using the Big Bang Nucleosynthesis observations, We infer an upper bound on the topological fluctuations in the spacetime foam vacuum $\sigma^2$, given by $\sigma^2 \lesssim 10^{-22}$.

##### 10.Enhancement of quantum gravity signal in an optomechanical experiment

**Authors:**Youka Kaku, Tomohiro Fujita, Akira Matsumura

**Abstract:** No experimental evidence of the quantum nature of gravity has been observed yet and a realistic setup with improved sensitivity is eagerly awaited. We find two effects, which can substantially enhance the signal of gravity-induced quantum entanglement, by examining an optomechanical system in which two oscillators gravitationally couple and one composes an optical cavity. The first effect comes from a higher-order term of the optomechanical interaction and generates the signal at the first order of the gravitational coupling in contrast to the second order results in previous works. The second effect is the resonance between the two oscillators. If their frequencies are close enough, the weak gravitational coupling effectively strengthens. Combining these two effects, the signal in the interference visibility could be amplified by a factor of $10^{24}$ for our optimistic parameters. The two effects would be useful in seeking feasible experimental setups to probe quantum gravity signals.

##### 11.Charged black string bounce and its field source

**Authors:**A. Lima, G. Alencar, R. N. Costa Filho, R. R. Landim

**Abstract:** This work builds upon the previous article [1] and explores the solution of the charged black string introduced in [2]. The black bounce regularization method, based on the Simpson-Visser solution, is employed by transforming the radial variable using $r\rightarrow \sqrt{r^2+a^2}$. The regular charged black string metric is defined, and the properties of event horizons, surface gravity, and Hawking temperature are investigated. The behavior of curvature quantities, including curvature invariants and tensors, is examined to verify the absence of singularities when $a\neq 0$. The Einstein equation for the energy-momentum tensor is solved, and the null energy condition is analyzed for the obtained solution. The sources of this solution are evaluated, combining a scalar field with nonlinear electrodynamics. However, unlike other works, an electric field is considered instead of a magnetic field. Finally, the study calculates the possibility of stable or unstable circular orbits for massive and massless particles.

##### 1.Quasinormal modes and echo effect of cylindrical anti-de Sitter black hole spacetime with a thin shell

**Authors:**Kai Lin

**Abstract:** This paper investigates the quasinormal mode (QNM) vibrations of a rotating cylindrical black hole (or black string) spacetime that is surrounded by a thin shell rotating synchronously with the black string's axis. The existence of the thin shell leads to a piecewise metric of the black hole spacetime beyond the horizon, which is divided into two stationary spacetime parts by the radius of the thin shell. As a result, the potential function $V(r)$ of the QNM equation is also discontinuous. To solve the QNM equation with the discontinuous potential function, we propose two methods, matrix method and generalized Horowitz-Hubeny Method. We find that the influence of the thin shell can reduce the QNM frequency of the black string while alleviating their amplitude decay rate. Our suggested method can be easily applied to other QNM calculations of black hole spacetime with discontinuous potential function, thus facilitating investigations into more intricate and realistic black hole spacetimes, such as those with accretion disks. Additionally, the finite difference method is employed to investigate the spacetime too. This analysis discloses a substantial gap in the potential function when the thin shell's mass and charge achieve sufficiently high values, resulting in the outer spacetime nearing gravitational collapse and extreme black hole scenarios. Within this gap, the QNM wave displays oscillations, producing an echo effect. Moreover, it is established that the closeness of the spacetime to the collapse threshold and charge extremality have positive correlation with the beat interval of this echo.

##### 2.Mixing of scalar and tensor metric perturbations

**Authors:**A. D. Dolgov, L. A. Panasenko

**Abstract:** Metric perturbations in General Relativity are usually separated into three distinct classes: scalar, vector, and tensor. In many cases these modes are separable, i.e. they satisfy independent equations of motion for each mode. However, in the present paper we argue that in many cases tensor and scalar modes are not separable, no matter what gauge conditions are chosen. The propagation of any of these mode depends on the other. A realistic example providing such mixing is presented.

##### 3.Test of conformal theory of gravity as an alternative paradigm to dark matter hypothesis from gravitational lensing studies

**Authors:**Shubhrangshu Ghosh, Mahasweta Bhattacharya, Yanzi Sherpa, Arunava Bhadra

**Abstract:** Weyl's conformal gravity theory, which is considered as a compelling alternative to general relativity theory, has been claimed to describe the observed flat rotation curve feature of spiral galaxies without the need of invoking dark matter. However, it is important to examine whether the Weyl theory can also explain the relevant gravitational lensing observations correctly without considering any dark matter. In this regard, the gravitational bending angle in static spherically space-time (Mannheim-Kazanas metric) in Weyl theory has been calculated by several authors over the last two decades, but the results are found largely divergent. In this work, we have revisited the problem and obtain the correct and consistent expression of the deflection angle in conformal gravity. Subsequently we perform the gravitational lensing analysis. We compare the prediction of Weyl gravity with the gravitational lensing observations of the rich galaxy clusters Abell 370 and Abell 2390 and is found that Weyl theory cannot describe the stated lensing observations without considering dark matter.

##### 4.How strings can explain regular black holes

**Authors:**Piero Nicolini

**Abstract:** This paper reviews the role of black holes in the context of fundamental physics. After recalling some basic results stemming from Planckian string calculations, I present three examples of how stringy effects can improve the curvature singularity of classical black hole geometries.

##### 5.Cosmologies with positive Lambda: Hierarchies of future behaviour

**Authors:**Helmut Friedrich

**Abstract:** Smooth Cauchy data for the Einstein-Lambda-vacuum field equations with positive cosmological constant Lambda that are sufficiently close to de Sitter data develop into a solution that admits a smooth conformal boundary Scri+ in its future. The conformal Einstein equations determine a smooth conformal extension across Scr+ that defines on `the other side' again a Lambda-vacuum solution. In this article we discuss to what extent these properties generalize to the future asymptotic behaviour of solutions to the Einstein-Lambda equations with matter. We study FLRW solutions and the Einstein-Lambda equations coupled to conformally covariant matter transport equations, to conformally privileged matter equations, and to conformally non-covariant matter equations. We present recent results on the Einstein-Lambda-perfect-fluid equations with a non-linear asymptotic dust or asymptotic radiation equation of state.

##### 6.First-order thermodynamics of scalar-tensor gravity

**Authors:**Serena Giardino, Andrea Giusti

**Abstract:** The first-order thermodynamics of scalar-tensor theory is a novel approach that exploits the intriguing relationship between gravity and thermodynamics to better understand the space of gravity theories. It is based on using Eckart's first-order irreversible thermodynamics on the effective imperfect fluid describing scalar-tensor gravity and characterises General Relativity as an equilibrium state, and scalar-tensor theories as non-equilibrium states, naturally describing the approach to equilibrium. Applications of this framework to cosmology, extensions to different classes of modified theories, and the formulation of two complementary descriptions based on the notions of temperature and chemical potential all contribute to a new and unifying picture of the landscape of gravity theories.

##### 7.Spherical collapse in scalar-Gauss-Bonnet gravity: taming ill-posedness with a Ricci coupling

**Authors:**Farid Thaalba, Miguel Bezares, Nicola Franchini, Thomas P. Sotiriou

**Abstract:** We study spherical collapse of a scalar cloud in scalar-Gauss-Bonnet gravity - a theory in which black holes can develop scalar hair if they are in a certain mass range. We show that an additional quadratic coupling of the scalar field to the Ricci scalar can mitigate loss of hyperbolicity problems that have plagued previous numerical collapse studies and instead lead to well-posed evolution. This suggests that including specific additional interactions can be a successful strategy for tackling well-posedness problems in effective field theories of gravity with nonminimally coupled scalars. Our simulations also show that spherical collapse leads to black holes with scalar hair when their mass is below a mass threshold and above a minimum mass bound and that above the mass threshold the collapse leads to black holes without hair, in line with results in the static case and perturbative analyses. For masses below the minimum mass bound we find that the scalar cloud smoothly dissipates, leaving behind flat space.

##### 1.Hawking radiation from stationary black holes using gravitational anomaly

**Authors:**Selim Sk, Sudipta Sarkar

**Abstract:** Among all the different techniques to derive the Hawking effect, the approach based on gravitational anomaly by Robinson and Wilczek provides a simple and satisfactory origin of the black hole radiation. In this picture, the effective near horizon physics becomes chiral and contains gravitational anomaly. Nevertheless, the underlying description must be generally covariant, and therefore we require a compensating energy-momentum flux whose divergence cancels the anomaly at the horizon. Remarkably, the energy flux associated with the Hawking emission from the horizon exactly cancels the gravitational anomaly and restores the general covariance at the quantum level. In this work, we present a generalization of the original derivation for a stationary axisymmetric black hole solution of any gravity theory which differs perturbatively from general relativity. The crucial input of the calculation is a remarkable simplification of the near horizon geometry and the validity of the zeroth law of black hole mechanics.

##### 2.Gravitational waves in scalar-tensor theory to one-and-a-half post-Newtonian order

**Authors:**David Trestini

**Abstract:** We compute the gravitational waves generated by compact binary systems in a class of massless scalar-tensor (ST) theories to the 1.5 post-Newtonian (1.5PN) order beyond the standard quadrupole radiation in general relativity (GR). Using and adapting to ST theories the multipolar-post-Minkowskian and post-Newtonian formalisms originally defined in GR, we obtain the tail and non-linear memory terms associated with the dipole radiation in ST theory. The multipole moments and GW flux of compact binaries are derived for general orbits including the new 1.5PN contribution, and comparison is made with previous results in the literature. In the case of quasi-circular orbits, we present ready-to-use templates for the data analysis of detectors, and for the first time the scalar GW modes for comparisons with numerical relativity results.

##### 3.Gravitational-wave tails of memory at 4PN order

**Authors:**David Trestini, Luc Blanchet

**Abstract:** We study a novel cubic nonlinear effect, the tails-of-memory, which consist of a combination of the tail effect (backscattering of linear gravitational waves against the curvature of spacetime generated by the source) and the memory effect (due to reradiation of gravitational waves by linear gravitational waves themselves). Our final result is consistent with a straightforward direct computation of the memory effect, but also involves many non-trivial tail-like terms.

##### 4.Cosmological models with arbitrary spatial curvature in the theory of gravity with non-minimal derivative coupling

**Authors:**Sergey V. Sushkov, Rafkat Galeev

**Abstract:** We investigate isotropic and homogeneous cosmological scenarios in the scalar-tensor theory of gravity with non-minimal derivative coupling of a scalar field to the curvature given by the term $(\zeta/H_0^2) G^{\mu\nu}\nabla_\mu\phi \nabla_\nu\phi$ in the Lagrangian. In general, a cosmological model is determined by six dimensionless parameters: the coupling parameter $\zeta$, and density parameters $\Omega_0$ (cosmological constant), $\Omega_2$ (spatial curvature term), $\Omega_3$ (non-relativistic matter), $\Omega_4$ (radiation), $\Omega_6$ (scalar field term), and the universe evolution is described by the modified Friedmann equation. In the case $\zeta=0$ (no non-minimal derivative coupling) and $\Omega_6=0$ (no scalar field) one has the standard $\Lambda$CDM-model, while if $\Omega_6\not=0$ -- the $\Lambda$CDM-model with an ordinary scalar field. The situation is crucially changed when the scalar field possesses non-minimal derivative coupling to the curvature, i.e. when $\zeta\not=0$. Now, depending on model parameters, (i) There are three qualitatively different initial state of the universe: an eternal kinetic inflation, an initial singularity, and a bounce. The bounce is possible for all types of spatial geometry of the homogeneous universe; (ii) For all types of spatial geometry, the universe goes inevitably through the primary quasi-de Sitter (inflationary) epoch when $a(t)\propto e^{h_{dS}(H_0t)} $ with the de Sitter parameter $h_{dS}^2={1}/{9\zeta}-{8\zeta\Omega_2^3}/{27\Omega_6}$. The mechanism of primary or kinetic inflation is provided by non-minimal derivative coupling and needs no fine-tuned potential; (iii) There are cyclic scenarios of the universe evolution with the non-singular bounce at a minimal value of the scale factor, and a turning point at the maximal one; (iv) There is a natural mechanism providing a change of cosmological epochs.

##### 5.Stability, quasinormal modes in a charged black hole in perfect fluid dark matter

**Authors:**Anish Das, Anirban Roy Chowdhury, Sunandan Gangopadhyay

**Abstract:** In this work, we study time-like and null geodesics in a charged black hole background immersed in perfect fluid dark matter (PFDM). Using the condition for circular geodesics, we evaluate the energy ($E$) and angular momentum ($L$) in terms of the radius ($r_c$) of the circular orbits. The existence and finite-ness of $E$ and $L$ constrain the possible range of PFDM parameter ($\chi$) and the radius of the circular orbit ($r_c$). We then use the Lyapunov exponent ($\lambda$) to study the stability of the geodesics. Then we analyze the critical exponent ($\gamma$) useful for determining the possibility of detection of gravitational wave signals. After that, we study the perturbation due to a massless scalar field in such a background and calculate the quasinrmal mode (QNM) frequencies and their dependence on PFDM parameter $\chi$ and black hole charge $Q$. Also, we compare the obtained QNM frequencies both in the exact case and in the eikonal limit. We also calculate the quality factor of the oscillating system and study its dependence on $\chi$ and $Q$. Finally, we evaluate the black hole shadow radius $R_s$ and graphically observe the effect of $\chi$ and $Q$ on it.

##### 6.A Cosmological Unicorn Solution to Finsler Gravity

**Authors:**Sjors Heefer, Christian Pfeifer, Antonio Reggio, Andrea Fuster

**Abstract:** We present a new family of exact vacuum solutions to Pfeifer and Wohlfarth's field equation in Finsler gravity, consisting of Finsler metrics that are Landsbergian but not Berwaldian, also known as unicorns due to their rarity. Interestingly we find that these solutions have a physically viable light cone structure, even though in some cases the signature is not Lorentzian but positive definite. We furthermore find a promising analogy between our solutions and classical FLRW cosmology. One of our solutions in particular has cosmological symmetry, i.e. it is spatially homogeneous and isotropic, and it is additionally conformally flat, with conformal factor depending only on the timelike coordinate. We show that this conformal factor can be interpreted as the scale factor, we compute it as a function of cosmological time, and we show that it corresponds to a linearly expanding (or contracting) Finsler universe.

##### 7.Gravitational collapse of matter in the presence of Quintessence and Phantom-like scalar fields

**Authors:**Priyanka Saha, Dipanjan Dey, Kaushik Bhattacharya

**Abstract:** In this work, we propose a model of the gravitational collapse of dark matter in the presence of quintessence or phantom-like scalar fields. Our treatment is based on the principles of general relativity up to virialization. We have chosen a spherical patch that starts to collapse gravitationally as it happens in top-hat collapse. It is seen that although the dark matter sector collapses the dark energy sector does keep a profile that is almost similar to the dark energy profile for the background expanding Friedmann-Lemaitre-Robertson-Walker (FLRW) universe for suitable model parameters. It is observed that in order to formulate the problem in the general relativistic setting one has to abandon the idea of a closed FLRW isolated collapsing patch. General relativity requires an external generalized Vaidya spacetime to be matched with the internal spherical patch whose dynamics is guided by the FLRW metric. It is shown that almost all collapses are accompanied by some flux of matter and radiation in the generalized Vaidya spacetime. Some of the spherical regions of the universe are seen not to collapse but expand eternally, producing void-like structures. Whether a spherical region will collapse or expand depends upon the initial values of the system and other model parameters. As this work shows that collapsing structures must emit some form of radiation, this may be taken as an observational signature of our proposal.

##### 8.Geometrothermodynamic cosmology

**Authors:**Orlando Luongo, Hernando Quevedo

**Abstract:** We review the main aspects of geometrothermodynamics, a formalism that uses contact geometry and Riemannian geometry to describe the properties of thermodynamic systems. We show how to handle in a geometric way the invariance of classical thermodynamics with respect to Legendre transformations, which means that the properties of the systems do not depend on the choice of the thermodynamic potential. Moreover, we show that in geometrothermodynamics it is possible to apply a variational principle to generate thermodynamic fundamental equations, which can be used in the context of relativistic cosmology to generate cosmological models. As a particular example, we consider a fundamental equation that relates the entropy with the internal energy and the volume of the Universe, and construct cosmological models with arbitrary parameters, which can be fixed to reproduce the main aspects of the inflationary era and the standard cosmological paradigm.

##### 9.Constraining Palatini gravity with GR-independent equations of state

**Authors:**Eva Lope-Oter, Aneta Wojnar

**Abstract:** We demonstrate how to construct GR-independent equations of state. We emphasize the importance of using theory-based principles instead of relying solely on astrophysical observables and General Relativity (GR). We build a set of equations of state based on first principles, including chiral perturbation theory and perturbation theory in quantum chromodynamics. Interpolation methods are employed to assume thermodynamic stability and causality in the intermediate region. These equations of state are then used to constrain quadratic Palatini $f(\mathcal R)$ gravity, indicating that the parameter lies within the range $-6.47 \lesssim \beta \lesssim 1.99$ km$^2$. Additionally, we briefly discuss the problem of phase transitions and twin stars.

##### 10.Cosmology in the Lorentz gauge theory

**Authors:**Tomi Koivisto

**Abstract:** This proceeding is an introduction to cosmological applications of the Lorentz gauge theory. It provides the ingredients for a unique, though yet tentative $\Lambda$CDM theory cosmology. The emergence of spacetime is described by the spontaneous symmetry breaking called here the khronogenesis. Space is then associated with the field strength of the antiself-dual gauge potential, and gravity is associated with the self-dual field strength. In the cosmological setting, khronogenesis seems to predict inflation. It is shown that the Lorentz gauge theory allows the consistent description of spin currents which could have important roles in cosmological phenomenology.

##### 1.On Chaplygin models in f(G) gravity

**Authors:**Fidele Twagirayezu, Abraham Ayirwanda, Albert Munyeshyaka, Solange Mukeshimana, Joseph Ntahompagaze, Leon Fidele Ruganzu Uwimbabazi

**Abstract:** The current work treats cosmological perturbation in a mixture of standard matter, Chaplygin gas as well as Gauss-bonnet fluids using a 1+3 covariant approach in the context of modified $f(G)$ gravity. We define the gradient variables to obtain linear perturbation equations. After scalar and redshift transformations, we consider both an original Chaplygin and generalized Chaplygin gas models under Gauss-bonnet gravity. For pedagogical purposes, the consideration of polynomial $f(G)$ gravity model was used to solve the perturbation equations for short- and long- wavelength modes and investigate the late time evolution. The numerical solutions were obtained. The results show that the energy overdensity perturbations decay with an increase in redshift. The treatment recovers GR results under limiting cases.

##### 2.Study of Boson Stars with Wormhole

**Authors:**Peng-Bo Ding, Tian-Xiang Ma, Yong-Qiang Wang

**Abstract:** In this paper, we reconsider the mixed system of BSs with wormholes at their center which performed by complex scalar field and phantom field and study a whole new condition about the potential. Both the symmetric and asymmetric solutions in the two asymptotically flat regions are obtained by using numerical method and we mainly explore the change of the results by varying the parameters of throats and potential. In ground state, we find there are multiple solutions at certain setting of parameters and with the increase of $\eta_0$ or decrease of $c$, the results gradually become single-valued functions and these two variables have similar influence to the curve shape of mass $M$ and charge $Q$, furthermore, the asymmetric solutions can turn into the solutions of symmetry at some frequency $\omega$ in certain $\eta_0$ and $c$. However, when it comes to excited state, the properties of solutions of symmetry is similar to the ground state while asymmetrical results exhibit altered characteristics. We also present the geometries of wormhole to investigate the property of this model.

##### 3.Multi-scale Constraints on Scalar-Field couplings to Matter: The Geodetic and Frame-Dragging Effects

**Authors:**David Benisty, Philippe Brax, Anne-Christine Davis

**Abstract:** The impact of light scalars coupled conformally and disformally to matter on the geodetic and frame-dragging (FD) precessions is calculated. For larger frequencies the disformal interaction becomes increasingly relevant. We use several satellite experiments and Pulsar time of arrival (ToA) measurements to derive bounds on the couplings, combining the Gravity Probe B, LARES, LAGEOS and GRACE results with pulsar timings. Forecasts for future constraints on the conformal and the disformal couplings based on the GINGER experiment, i.e. a future measurement of the Sagnac effect on Earth, the motion of $S$-stars around the galactic centre and future pulsar timing observations are presented.

##### 4.Tripotential MOND theories

**Authors:**Mordehai Milgrom

**Abstract:** I present a new class of nonrelativistic, modified-gravity MOND theories. The three gravitational degrees of freedom of these ``TRIMOND'' theories are the MOND potential and two auxiliary potentials, one of which emerges as the Newtonian potential. Their Lagrangians involve a function of three acceleration variables -- the gradients of the potentials. So, the transition from the Newtonian to the MOND regime is rather richer than in the aquadratic-Lagrangian theory (AQUAL) and the quasilinear MOND theory (QUMOND), which are special cases of TRIMOND, each defined by a Lagrangian function of a single variable. In particular, unlike AQUAL and QUMOND whose deep-MOND limit (DML) is fully dictated by the required scale invariance, here, the scale-invariant DML still requires specifying a function of two variables. For one-dimensional (e.g., spherical) mass distributions, in all TRIMOND theories the MOND acceleration is a (theory specific, but system independent) function of the Newtonian acceleration; their variety appears in nonsymmetric situations. Also, they all make the salient, primary MOND predictions. For example, they predict the same DML virial relation as AQUAL and QUMOND, and thus the same DML $M-\sigma$ relation, and the same DML two-body force. Yet they can differ materially on secondary predictions. Such TRIMOND theories may be the nonrelativistic limits of scalar-bimetric relativistic formulations of MOND, such as BIMOND with an added scalar.

##### 1.Entanglement partners and monogamy in de Sitter universes

**Authors:**Yasusada Nambu, Koji Yamaguchi

**Abstract:** We investigate entanglement of local spatial modes defined by a quantum field in a de Sitter universe. The introduced modes show dis-entanglement behavior when the separation between two regions where local modes are assigned becomes larger than the cosmological horizon. To understand the emergence of separability between these local modes, we apply the monogamy inequality proposed by S. Camalet. We embed the focusing bipartite mode defined by the quantum field in a pure four-mode Gaussian state, and identify its partner modes. Then applying a Gaussian version of the monogamy relation, we show that the external entanglement between the bipartite mode and its partner modes constrains the entanglement of the bipartite mode. Thus the emergence of separability of local modes in the de Sitter universe can be understood from the perspective of entanglement monogamy.

##### 2.Gravitational lensing aided luminosity distance estimation for compact binary coalescences

**Authors:**Kyungmin Kim, Eungwang Seo, Chunglee Kim

**Abstract:** The luminosity distance is a key observable of gravitational-wave observations. We demonstrate how one can correctly retrieve the luminosity distance of compact binary coalescences if the gravitational-wave signal is strongly lensed. We perform a proof-of-concept parameter estimation for the luminosity distance supposing (i) strong lensing produces two lensed gravitational-wave signals, (ii) the advanced LIGO-Virgo network detects both lensed signals as independent events, and (iii) the two events are identified as strongly lensed signals originated from a single compact binary coalescence. Focusing on the maximum magnification allowed in the given lensing scenario, we find that the strong lensing can improve the precision of the distance estimation by up to a factor of two compared to that can be expected for the signal experiencing no lensing. Our results imply that strong lensing of gravitational waves can be helpful for better constraining the distance to the source, and furthermore, the Hubble constant.

##### 3.Bilocal geodesic operators as a tool of investigating the optical properties of spacetimes

**Authors:**Julius Serbenta

**Abstract:** In my thesis, I present one particular example of the formalism capable of describing the propagation of a family of light rays in a curved spacetime. It is based on the resolvent operator of the geodesic deviation equation for null geodesics which is known as the bilocal geodesic operator (BGO) formalism. The BGO formalism generalizes the standard treatment of light ray bundles by allowing observations extended in time or performed by a family of neighbouring observers. Furthermore, it provides a more unified picture of relativistic geometrical optics and imposes a number of consistency requirements between the optical observables. The thesis begins with a brief introduction of the transfer matrix and its relativistic versions known as the Jacobi propagators and the bilocal geodesic operators. Then the basics of differential geometry are reviewed, with an emphasis on the geometry of the tangent bundle and the geodesic flow, which later provide the foundation for the BGO formalism. The mathematical introduction is then followed by two articles about the applications of the BGO formalism in the studies of optical distance measures and the conclusion.

##### 4.Gravitational traces of bumblebee gravity in metric-affine formalism

**Authors:**A. A. Araújo Filho, H. Hassanabadi, N. Heidari, J. Kríz, P. J. Porfírio, S. Zare

**Abstract:** This work explores various manifestations of bumblebee gravity within the metric--affine formalism. We investigate the impact of Lorentz violation parameter, denoted as $X$, on the modification of the \textit{Hawking} temperature. Our calculations reveal that as $X$ increases, the values of the \textit{Hawking} temperature attenuate. To examine the behavior of massless scalar perturbations, specifically the \textit{quasinormal} modes, we employ the WKB method. The transmission and reflection coefficients are determined through our calculations. The outcomes indicate that a stronger Lorentz--violating parameter results in slower damping oscillations of gravitational waves. To comprehend the influence of the \textit{quasinormal} spectrum on time--dependent scattering phenomena, we present a detailed analysis of scalar perturbations in the time--domain solution. Additionally, we conduct an investigation on shadows, revealing that larger values of $X$ correspond to larger shadow radii. Lastly, we explore the concept of time delay within this framework.

##### 5.Spherically-symmetric geometries in a matter reference frame as quantum gravity condensates

**Authors:**Daniele Oriti, Yi-Li Wang

**Abstract:** Candidate microstates of a spherically symmetric geometry are constructed in the group field theory formalism for quantum gravity, for models including both quantum geometric and scalar matter degrees of freedom. The latter are used as a material reference frame to define the spacetime localization of the various elements of quantum geometry. By computing quantum geometric observables, we then match the quantum states with a spherically symmetric classical geometry, written in a suitable matter reference frame.

##### 6.The classical and quantum implications of the Raychaudhuri Equation in f(T)-gravity

**Authors:**Madhukrishna Chakraborty, Subenoy Chakraborty

**Abstract:** The present work deals with the classical and quantum aspects of the Raychaudhuri equation in the framework of f(T)-gravity theory. In the background of homogeneous and isotropic Friedmann Lemaitre Robertson Walker space time, the Raychaudhuri equation has been formulated and used to examine the focusing theorem and convergence condition for different choices of f(T). Finally in quantum cosmology, the wave function of the universe has been shown to be the energy eigen function of the time independent Schrodinger equation of a particle. Also probability measure on the mini-super space has been examined at zero volume for singularity analysis in the quantum regime. Lastly the Bohmian trajectory for the present quantum system has been explicitly determined for some particular choices.

##### 7.Rapid identification of time-frequency domain gravitational wave signals from binary black holes using deep learning

**Authors:**Shang-Jie Jin, Yu-Xin Wang, Tian-Yang Sun, Jing-Fei Zhang, Xin Zhang

**Abstract:** Recent developments in deep learning techniques have offered an alternative and complementary approach to traditional matched filtering methods for the identification of gravitational wave (GW) signals. The rapid and accurate identification of GW signals is crucial for the progress of GW physics and multi-messenger astronomy, particularly in light of the upcoming fourth and fifth observing runs of LIGO-Virgo-KAGRA. In this work, we use the 2D U-Net algorithm to identify the time-frequency domain GW signals from stellar-mass binary black hole (BBH) mergers. We simulate BBH mergers with component masses from 5 to 80 $M_{\odot}$ and account for the LIGO detector noise. We find that the GW events in the first and second observation runs could all be clearly and rapidly identified. For the third observation run, about $80\%$ GW events could be identified and GW190814 is inferred to be a BBH merger event. Moreover, since the U-Net algorithm has advantages in image processing, the time-frequency domain signals obtained through U-Net can preliminarily determine the masses of GW sources, which could help provide the mass priors for future parameter inferences. We conclude that the U-Net algorithm could rapidly identify the time-frequency domain GW signals from BBH mergers and provide great help for future parameter inferences.

##### 8.From Bardeen-boson stars to black holes without event horizon

**Authors:**X. E. Wang

**Abstract:** In a talk given in 2013, S. Hawking conjectured that the event horizon of black holes does not exist and suggested redefining black holes as bound states of the gravitational field. Inspired by this idea, we investigated the coupling of the Bardeen action and a complex scalar field model. Numerically, we obtained a class of boson stars solutions with the magnetic monopole charge $q$. When the constant $q$ exceeds a certain threshold, we observed that as the frequency approaches zero, a critical position $r_c$ emerges where the scalar field concentrates within its interior. Outside this critical position, these boson star solutions tend to infinitely approach what is known as an extreme black hole. However, there is no event horizon present. While our results are model-dependent and their generality remains uncertain, they align well with Hawking's conjecture that real, regular black holes do not have an event horizon and provided valuable insights into the understanding and development of concepts such as fuzzballs, firewalls and black hole soft hairs.

##### 9.Dynamical stability in models where dark matter and dark energy are non-minimally coupled to curvature

**Authors:**Saddam Hussain, Anirban Chatterjee, Kaushik Bhattacharya

**Abstract:** This work explores the dynamical stability of cosmological models where dark matter and dark energy can non-minimally couple to spacetime (scalar) curvature. Two different scenarios are presented here. In the initial case, only dark matter sector is coupled to curvature in the presence of a quintessence scalar field. In the second case both dark matter and the quintessence field are coupled to curvature. It is shown that one can get an accelerating expansion phase of the universe in both the cases. The nature of the fixed points show that there can be stable or unstable phases where the curvature coupling vanishes and dark energy and dark matter evolve independently. On the other hand there can be stable accelerating expansion phases where both the components are coupled to curvature.

##### 10.Einstein and Jordan frame correspondence in quantum cosmology: Expansion-collapse duality

**Authors:**Dipayan Mukherjee, Harkirat Singh Sahota

**Abstract:** The conformal correspondence between FLRW universes in the Einstein and Jordan frames allows for an expansion-collapse duality -- an always expanding Einstein frame universe can have a dual Jordan frame description that is contracting forever. The scenario eventually runs into an apparent paradox. When a collapsing universe approaches singularity, the classical description of the spacetime becomes inadequate. The contracting Jordan frame universe is expected to develop quantum characteristics when its scale factor becomes sufficiently small. However, at the same time, the corresponding Einstein frame universe is expected to behave classically, due to the arbitrarily large size it has grown to. In this case, the conformal map appears to be providing a duality between a quantum effect-dominated universe and a universe behaving classically. We investigate the status of the conformal map at the quantum level in such a scenario, focusing on addressing this paradox. The Einstein and Jordan frame universes are quantized individually using the Wheeler-DeWitt prescription. We show that the classical conformal map holds true at the quantum level when compared through the expectation values of the scale factor operators in the two frames. The relative quantum fluctuation in the scale factor is found to be conformally invariant, and it increases in both the past and future directions according to the internal clock. Expectedly, the quantum fluctuations in the collapsing Jordan frame keep on increasing as it shrinks towards singularity. More surprisingly, the quantum fluctuations in the expanding Einstein frame keep on increasing as well, even as its classical scale factor becomes larger. Despite having drastically different cosmological evolutions, the rise in quantum characteristics in a collapsing frame implies the same in its expanding counterpart, thereby resolving the apparent paradox.

##### 11.From inflation to reheating and their dynamical stability analysis in Gauss-Bonnet gravity

**Authors:**Sergei D. Odintsov, Tanmoy Paul

**Abstract:** We investigate the inflation and reheating phenomenology in scalar-Einstein-Gauss-Bonnet theory of gravity where a scalar field non-minimally couples with the Gauss-Bonnet (GB) curvature term. Regarding the inflationary phenomenology, we find -- (1) the inflation starts with a quasi de-Sitter phase and has an exit at a finite e-fold, (2) the scalar and tensor perturbations prove to be ghost free and do not suffer from gradient instability, (3) the curvature perturbation amplitude as well as its tilt and the tensor-to-scalar ratio turn out to be simultaneously compatible with the recent Planck data for suitable values of the parameters. After the inflation ends, the scalar field starts to decay to radiation with a constant decay width. For our considered scalar potential and the GB coupling function, the model results to an analytic power law solution of the Hubble parameter and a logarithmic solution of the scalar field during the reheating era, where the exponent of the Hubble parameter determines the effective EoS parameter ($w_\mathrm{eff}$) during the same. The stability of such reheating dynamics is examined by dynamical analysis which ensures that $w_\mathrm{eff}$ can go beyond unity and reach up-to the maximum value of $\mathrm{max}(w_\mathrm{eff}) = 1.56$. The scenario with $w_\mathrm{eff} > 1$ proves to be purely due to the presence of the GB coupling function, which in turn may have important consequences on enhancing the primordial gravitational waves' amplitude observed today. The inflationary e-fold number gets further constrained by the input of the reheating stage. We finally construct the complete forms of scalar potential ($V(\phi)$) and the GB coupling ($\xi(\phi)$) function that smoothly transits from inflation to reheating, and numerically solve the Hubble parameter and the scalar field for such complete forms of $V(\phi)$ and $\xi(\phi)$.

##### 12.Perturbations in Horndeski theory above anisotropic cosmological background

**Authors:**S. Mironov, A. Shtennikova

**Abstract:** In this paper we have constructed the unconstrained action for the perturbations above Bianchi I type background in the most general scalar-tensor theory of gravity, the Horndeski theory. The result could be used now in the context of anisotropic early Universe models, no-go theorems and general stability and in anisotropic probes of current cosmological perturbations.

##### 1.Quasinormal mode spectrum of the AdS black hole with the Robin boundary condition

**Authors:**Shunichiro Kinoshita, Tomohiro Kozuka, Keiju Murata, Keita Sugawara

**Abstract:** We study the quasinormal mode (QNM) spectrum of an asymptotically AdS black hole with the Robin boundary condition at infinity. We consider the Schwarzshild-AdS$_4$ with the flat event horizon as the background spacetime and study its scalar field perturbation. Denoting leading coefficients of slow- and fast-decay modes of the scalar field at infinity as $\phi_1$ and $\phi_2$, respectively, we assume a linear relation between them as $\phi_2 = \cot(\theta/2) \phi_1$, where $\theta$ is a constant called the Robin parameter and periodic under $\theta\sim\theta+2\pi$. In a certain range of the Robin parameter, there is an instability driven by the boundary condition. We also find the holonomy in the QNM spectrum under the parametric cycle of the boundary condition: $\theta=0\to2\pi$. After the one-cycle, $n$-th overtone of the QNM moves to $(n-1)$-th overtone. The fundamental tone of the QNM is swept out to the infinity in the complex plane.

##### 2.Bypassing Bekenstein's no-scalar-hair theorem without violating the energy conditions

**Authors:**Panagiotis Dorlis, Nick E. Mavromatos, Sotirios-Neilos Vlachos

**Abstract:** In this work we establish in a rigorous manner, and a model independent way, the conditions for bypassing Bekenstein's no-scalar-hair theorem for static, spherically symmetric, and asymptotically flat black holes, while maintaining the validity of the energy conditions. Specifically, we argue that a hidden assumption in the theorem, namely the vanishing of the quantity $\mathcal{G} = \mathcal{E} + T^\theta\!_\theta$, where $\mathcal{E}$ is the energy density and $T^\theta\!_\theta$ the corresponding component of the energy-momentum tensor of the scalar field theory, can be relaxed. Indeed, if $\mathcal{G}$ is positive, as a consequence of the assumption on the validity of the energy conditions, then scalar hair is potentially allowed in the black hole's exterior, consistently with the gravitational equations and the generic properties of the (non-trivial) energy momentum tensor. As an explicit example, in which such a behaviour is realised, we discuss the well known model of a (3+1)-dimensional Schwarzschild black hole coupled to a spontaneously broken Yang-Mills $SU (2)$ gauge theory interacting with a Higgs scalar. We present a rather novel approach to obtain analytical black hole solutions for this system (in contrast to the numerical ones in the existing literature) by applying an appropriate perturbative treatment whereby the black hole configuration is derived as a result of backreaction of Higgs and gauge fields onto an initially fixed flat spacetime. The massive nature of the scalar and gauge fields in this example requires a special treatment, because of their asymptotic form, which we discuss in some detail.

##### 3.Uniform sky glow (CMB) observed through the throat of a wormhole

**Authors:**Mikhail A. Bugaev, Igor D. Novikov, Serge V. Repin, Polina S. Samorodskaya

**Abstract:** The problem of the possibility of observing a uniform sky glow through the throat of a Morris--Thorne wormhole by an observer located in another asymptotically flat space-time is considered. It is shown that an individual star has multiple images, and the image of a luminous sky has a complex structure and contains ring structures. The reasons for the emergence of such structures are considered. The distribution of radiation intensity in the image along the radial coordinate is constructed.In addition, an image of the Morris-Thorne wormhole was constructed against the background of uniform sky radiation in the observer's space. A comparison to observations can be made by producing a synthetic Morris-Thorne type wormhole image against a CMB background. This image has been constructed by a combination of the images for inner and outer areas.

##### 4.LISA stellar-mass black hole searches with semi-coherent and particle-swarm methods

**Authors:**Diganta Bandopadhyay, Christopher J. Moore

**Abstract:** This paper considers the problem of searching for quiet, long-duration and broadband gravitational wave signals, such as stellar-mass binary black hole binaries, in mock LISA data. We propose a method that combines a semi-coherent likelihood with the use of a particle swarm optimizer capable of efficiently exploring a large parameter space. The semi-coherent analysis is used to widen the peak of the likelihood distribution over parameter space, congealing secondary peaks and thereby assisting in localizing the posterior bulk. An iterative strategy is proposed, using particle swarm methods to initially explore a wide, loosely-coherent likelihood and then progressively constraining the signal to smaller regions in parameter space by increasing the level of coherence. The properties of the semi-coherent likelihood are first demonstrated using the well-studied binary neutron star signal GW170817. As a proof of concept, the method is then successfully applied to a simplified search for a stellar-mass binary black hole in zero-noise LISA data. Finally, we conclude by discussing what remains to be done to develop this into a fully-capable search and how the method might also be adapted to tackle the EMRI search problem in LISA.

##### 5.Testing space-time geometries and theories of gravity at the Galactic Center with pulsar's time delay

**Authors:**Riccardo Della Monica, Ivan de Martino, Mariafelicia de Laurentis

**Abstract:** We developed a numerical methodology to compute the fully-relativistic propagation time of photons emitted by a pulsar in orbit around a massive compact object, like the supermassive black hole Sagittarius A* in the Galactic Center, whose gravitational field is described by a generic spherically symmetric space-time. Pulsars at the Galactic Center are usually regarded as the next major precision probe for theories of gravity, filling the current experimental gap between horizon-scale gravity tests and those at larger scales. We retain a completely general approach, which allows us to apply our code to the Schwarzschild space-time (by which we successfully validate our methodology) and to three different well-motivated alternatives to the standard black hole paradigm. The results of our calculations highlight departures spanning several orders of magnitudes in timing residuals, that are supposed to be detectable with future observing facilities like the Square Kilometer Array.

##### 6.Constraining the quantum gravity polymer scale using LIGO data

**Authors:**Angel Garcia-Chung, Matthew F. Carney, James B. Mertens, Aliasghar Parvizi, Saeed Rastgoo, Yaser Tavakoli

**Abstract:** We present the first empirical constraints on the polymer scale describing polymer quantized GWs propagating on a classical background. These constraints are determined from the polymer-induced deviation from the classically predicted propagation speed of GWs. We leverage posterior information on the propagation speed of GWs from two previously reported sources: 1) inter-detector arrival time delays for signals from the LIGO-Virgo Collaboration's first gravitational-wave transient catalog, GWTC1, and 2) from arrival time delays between GW signal GW170817 and its associated gamma-ray burst GRB170817A. For pure-GW constraints, we find relatively uninformative combined constraints of $\nu = 0.96\substack{+0.15 \\ -0.21} \times 10^{-53} \, \rm{kg}^{1/2}$ and $\mu = 0.94\substack{+0.75 \\ -0.20} \times 10^{-48} \, \rm{kg}^{1/2} \cdot s$ at the $90\%$ credible level for the two polymer quantization schemes, where $\nu$ and $\mu$ refer to polymer parameters associated to the polymer quantization schemes of propagating gravitational degrees of freedom. For constraints from GW170817/GRB170817A, we report much more stringent constraints of $\nu_{\mathrm{low}} =2.66\substack{+0.60 \\ -0.10}\times 10^{-56}$, $\nu_{\mathrm{high}} = 2.66\substack{+0.45 \\ -0.10}\times 10^{-56} $ and $\mu_{\mathrm{low}} = 2.84\substack{+0.64 \\ -0.11}\times 10^{-52}$, $\mu_{\mathrm{high}} = 2.76\substack{+0.46 \\ -0.11}\times 10^{-52}$ for both representations of polymer quantization and two choices of spin prior indicated by the subscript. Additionally, we explore the effect of varying the lag between emission of the GW and EM signals in the multimessenger case.

##### 7.Electromagnetic field of a charge asymptotically approaching spherically symmetric black hole

**Authors:**Komarov S. O., Gorbatsievich A. K., Vereshchagin G. V

**Abstract:** We consider a test charged particle falling onto a Schwarzschild black hole and evaluate its electromagnetic field. The Regge-Wheeler equation is solved analytically by approximating the potential barrier with Dirac delta function and rectangular barrier. We show that for asymptotically large time measured by a distant observer the electromagnetic field approaches the spherically symmetric electrostatic field exponentially fast. This implies that in the region accessible to a distant observer the initial state of separated charge and Schwarzschild black hole becomes asymptotically indistinguishable from the Reisnner-Nordstr\"om solution. Implications of this result for models with plasma accretion on black holes are discussed.7 a

##### 8.Background Filter: A method for removing signal contamination during significance estimation of a GstLAL anaysis

**Authors:**Prathamesh Joshi, Leo Tsukada, Chad Hanna

**Abstract:** To evaluate the probability of a gravitational-wave candidate originating from noise, GstLAL collects noise statistics from the data it analyzes. Gravitational-wave signals of astrophysical origin get added to the noise statistics, harming the sensitivity of the search. We present the Background Filter, a novel tool to prevent this by removing noise statistics that were collected from gravitational-wave candidates. To demonstrate its efficacy, we analyze one week of LIGO and Virgo O3 data, and show that it improves the sensitivity of the analysis by 20-40% in the high mass region, in the presence of 868 simulated gravitational-wave signals. With the upcoming fourth observing run of LIGO, Virgo, and KAGRA expected to yield a high rate of gravitational-wave detections, we expect the Background Filter to be an important tool for increasing the sensitivity of a GstLAL analysis.

##### 9.Regular black holes in Einstein cubic gravity

**Authors:**L. A. Lessa, J. E. G. Silva

**Abstract:** We investigate the effects of the Einstein cubic gravity (ECG) on regular black hole solutions driven by nonlinear electrodynamics (NLE) sources. The ECG tends to form a naked singularity at the origin for a high ECG coupling constant. Assuming that ECG provides only perturbative corrections to the regular magnetic charged solutions, we found modified regular solutions with a de Sitter-like core whose cosmological constant depends on the magnetic charge and the ECG coupling constant. The thermodynamic stability is investigated by means of the Hawking temperature and the heat capacity. In fact, for a small charge and ECG coupling, the Hawking temperature is regularized, leaving a thermodynamic stable remnant for a small $r_h \neq 0$. The heat capacity reveals that the ECG regular black hole undergoes a phase transition between an unstable into a stable configuration.

##### 10.Gravitational Pair Production and Black Hole Evaporation

**Authors:**Michael F. Wondrak, Walter D. van Suijlekom, Heino Falcke

**Abstract:** We present a new avenue to black hole evaporation using a heat-kernel approach analogous as for the Schwinger effect. Applying this method to an uncharged massless scalar field in a Schwarzschild spacetime, we show that spacetime curvature takes a similar role as the electric field strength in the Schwinger effect. We interpret our results as local pair production in a gravitational field and derive a radial production profile. The resulting emission peaks near the unstable photon orbit. Comparing the particle number and energy flux to the Hawking case, we find both effects to be of similar order. However, our pair production mechanism itself does not explicitly make use of the presence of a black hole event horizon.

##### 11.Slowly-rotating compact objects: the nonintegrability of Hartle-Thorne particle geodesics

**Authors:**Kyriakos Destounis, Kostas D. Kokkotas

**Abstract:** X-ray astronomy provides information regarding the electromagnetic emission of active galactic nuclei and X-ray binaries. These events provide details regarding the astrophysical environment of black holes and stars, and help us understand gamma-ray bursts. They produce estimates for the maximum mass of neutron stars and eventually will contribute to the discovery of their equation of state. Thus, it is crucial to study these configurations to increase the yield of X-ray astronomy when combined with multimessenger gravitational-wave astrophysics and black hole shadows. Unfortunately, an exact solution of the field equations does not exist for neutron stars. Nevertheless, there exist a variety of approximate compact objects that may characterize massive or neutron stars. The most studied approximation is the Hartle-Thorne metric that represents slowly-rotating compact objects, like massive stars, white dwarfs and neutron stars. Recent investigations of photon orbits and shadows of such metric revealed that it exhibits chaos close to resonances. Here, we thoroughly investigate particle orbits around the Hartle-Thorne spacetime. We perform an exhaustive analysis of bound motion, by varying all parameters involved in the system. We demonstrate that chaotic regions, known as Birkhoff islands, form around resonances, where the ratio of the radial and polar frequency of geodesics, known as the rotation number, is shared throughout the island. This leads to the formation of plateaus in rotation curves during the most prominent $2/3$ resonance, which designate nonintegrability. We measure their width and show how each parameter affects it. The nonintegrability of Hartle-Thorne metric may affect quasiperiodic oscillations of low-mass X-ray binaries, when chaos is taken into account, and improve estimates of mass, angular momentum and multipole moments of astrophysical compact objects.

##### 12.Neural Posterior Estimation with guaranteed exact coverage: the ringdown of GW150914

**Authors:**Marco Crisostomi, Kallol Dey, Enrico Barausse, Roberto Trotta

**Abstract:** We analyze the ringdown phase of the first detected black-hole merger, GW150914, using a simulation-based inference pipeline based on masked autoregressive flows. We obtain approximate marginal posterior distributions for the ringdown parameters, namely the mass, spin, and the amplitude and phases of the dominant mode and its first overtone. Thanks to the locally amortized nature of our method, we are able to calibrate our posteriors with injected simulations, producing posterior regions with guaranteed (i.e. exact) frequentist coverage of the true values. For GW150914, our calibrated posteriors provide only mild evidence (~ 2 sigma) for the presence of an overtone, even if the ringdown is assumed to start at the peak of the amplitude.

##### 13.Gravity as a Statistical Manifold/ On a bi-Connection Formulation of Gravitation

**Authors:**Damianos Iosifidis, Konstantinos Pallikaris

**Abstract:** We formulate a bi-Connection Theory of Gravity whose Gravitational action consists of a recently defined mutual curvature scalar. Namely, we build a gravitational theory consisting of one metric and two affine connections, in a Metric-Affine Gravity setup. Consequently, coupling the two connections on an equal footing with matter, we show that the geometry of the resulting theory is, quite intriguingly, that of Statistical Manifold. This ultimately indicates a remarkable mathematical correspondence between Gravity and Information Geometry.

##### 1.Dynamical dark energy can amplify the expansion rate of the Universe

**Authors:**Hai-Chao Zhang

**Abstract:** By adding a matter-coupled dark energy field to Einstein's General Relativity (GR), this paper proves that the dynamical dark energy field can change the frequency of photons from distant galaxies as well as from background radiation of remote Universe. Therefore, when the observed frequency-shift of the photons is entirely attributed to the temporal variation of the cosmic scale factor, the calculated expansion rate of the Universe will be slightly greater than its actual value. The predicted values of the temperature of the cosmic blackbody radiation in the past (future) of the Universe are slightly larger (gradually smaller and smaller) than those in the standard cosmology. Since the blackbody radiation becomes the present cosmic microwave background (CMB) and its present-day temperature is directly estimated according to the Planck's law of blackbody radiation, the measured value of the CMB temperature is independent of whether to consider the scalar field or not.

##### 2.$4D$ Einstein-Gauss-Bonnet Black Hole in Power-Yang-Mills Field: A Shadow Study

**Authors:**M. Zubair, Muhammad Ali Raza, Furkat Sarikulov, Javlon Rayimbaev

**Abstract:** We consider a static black hole immersed in the Power-Yang-Mills field in four dimensional Einstein-Gauss-Bonnet gravity and investigate the effect of various parameters on the radius of the photon sphere. The modified form of the Newman-Janis algorithm is used for obtaining a rotating black hole solution in this gravity. Further, we try to explore the influence of the Yang-Mills magnetic charge $Q$ with power $q$, Gauss-Bonnet parameter $\alpha$ and spin $a$ on the horizon radius. The geodesic equations are constructed by incorporating the Hamilton-Jacobi formalism. The radial component of the geodesic equations gives the effective potential which is further used in deriving the mathematical structure for the shadows by using Bardeen's procedure for a fixed observer at infinity. The shadows are calculated and plotted in terms of two celestial coordinates for an equatorial observer. It is observed that all the parameters have a very significant effect on the shadow and related physical observables. {We also obtain the constraint values for the spin, magnetic charge and Gauss-Bonnet parameters, using the shadow size of supermassive black holes Sagittarius A$^*$ and M$87$* from the EHT observations for the cases of $q=0.6$ and $0.9$. It is shown that there are upper and lower bounds for the charge and spin of M$87$* at $q=0.6$, while only the upper bounds for charge and spin of Sagittarius A$^*$. Finally, we investigate the energy emission rate in the Hawking radiation around the $4D$ Einstein-Gauss-Bonnet black hole in the Power-Yang-Mills field.}

##### 3.Volume Singularities in General Relativity

**Authors:**Leonardo García-Heveling

**Abstract:** We propose a new notion of singularity in General Relativity which complements the usual notions of geodesic incompleteness and curvature singularities. Concretely, we say that a spacetime has a volume singularity if there exist points whose future or past has arbitrarily small spacetime volume: In particular, smaller than a Planck volume. From a cosmological perspective, we show that the (geodesic) singularities predicted by Hawking's theorem are also volume singularities. In the black hole setting, we show that volume singularities are always shielded by an event horizon, prompting a discussion of Penrose's cosmic censorship conjectures.

##### 4.Rotating black holes embedded in a cosmological background for scalar-tensor theories

**Authors:**Eugeny Babichev, Christos Charmousis, Nicolas Lecoeur

**Abstract:** We present solutions of DHOST theories describing a rotating black hole embedded in an expanding universe. The solution is constructed by conformal transformation of a stealth Kerr(-de Sitter) black hole. The conformal factor depends explicitly on the scalar field -- but not on its derivative -- and defines the new theory. The scalar field of the stealth Kerr(-de Sitter) solution depends on time, leading to the time-dependence of the obtained conformal metric, with cosmological asymptotics at large distances. We study the properties of the obtained metric by considering regular null geodesic congruences, and identify trapping black hole and cosmological horizons.

##### 5.Critical phenomena in the collapse of gravitational waves

**Authors:**Thomas W. Baumgarte, Bernd Brügmann, Daniela Cors, Carsten Gundlach, David Hilditch, Anton Khirnov, Tomáš Ledvinka, Sarah Renkhoff, Isabel Suárez Fernández

**Abstract:** Fine-tuning generic but smooth spherically-symmetric initial data for general relativity to the threshold of dynamical black hole formation creates arbitrarily large curvatures, mediated by a universal self-similar solution that acts as an intermediate attractor. For vacuum gravitational waves, however, these critical phenomena have been elusive. We present, for the first time, excellent agreement among three independent numerical simulations of this collapse. Surprisingly, we find no universality, and observe approximate self-similarity for some families of initial data but not for others.

##### 6.Accretion onto a static spherically symmetric regular MOG dark compact object

**Authors:**Kourosh Nozari, Sara Saghafi, Fateme Aliyan

**Abstract:** In astrophysics, the process of a massive body acquiring matter is referred to as accretion. The extraction of gravitational energy occurs as a result of the infall. Since it converts gravitational energy into radiation, accretion onto dark compact objects, e.g. black holes, neutron stars, and white dwarfs is an extremely significant process in the astrophysical context. Accretion process is a fruitful way to explore the features of modified gravity (MOG) theories by testing the behavior of their solutions associated with dark compact objects. In this paper, we study the motion of electrically neutral and charged particles moving in around a regular spherically symmetric MOG dark compact object to explore their related innermost stable circular orbit (ISCO) and energy flux. Then, we turn to investigate the accretion of perfect fluid onto the regular spherically symmetric MOG dark compact object. We obtain analytical expressions for four-velocity and proper energy density of the accreting fluid. We see that the MOG parameter increases the ISCO radius of either electrically neutral or charged test particles while it decreases the corresponding energy flux. Moreover, the energy density and the radial component of the four-velocity of the infalling fluid decrease by increasing the MOG parameter near the central source.

##### 7.A new class of regular Black Holes in Einstein Gauss Bonnet gravity with localized sources of matter

**Authors:**Milko Estrada, Rodrigo Aros

**Abstract:** We provide a new regular black hole solution (RBH) in Einstein Gauss Bonnet (EGB) gravity with presence of localized sources of matter in the energy momentum tensor. We determinate the necessary constraints in order that the solution to be regular. Although we use a specific form for the energy density as test of prove, these constraints could serve as a recipe for constructing several new RBH solutions in EGB gravity with localized sourced. Due that the usual first law of thermodynamics is not valid for RBH, we rewrite the first law for EGB, which leads to correct values of entropy and volume. The size of the extremal black hole, whose temperature vanishes, becomes smaller for larger dimensions, whose radius could be of order of the Planck units, thus the evaporation would stop once the horizon radius contracts up to a value close to the Planck length, which could be related with the apparition of quantum effects. Furthermore, the presence of matter fields in the energy momentum tensor induces two phase transitions, where there are two regions of stability. This differs from the vacuum EGB solution, where the specific heat is always negative without phase transition as occurs in Schwarzschild black hole.

##### 8.Asymptotically locally flat and AdS higher-dimensional black holes of Einstein-Horndeski-Maxwell gravity in the light of EHT observations: shadow behavior and deflection angle

**Authors:**Kourosh Nozari, Sara Saghafi

**Abstract:** Unification of gravity with other interactions, achieving the ultimate framework of quantum gravity, and fundamental problems in particle physics and cosmology motivate to consider extra spatial dimensions. The impact of these extra dimensions on the modified theories of gravity has attracted a lot of attention. One way to examine how extra dimensions affect the modified gravitational theories is to analytically investigate astrophysical phenomena, such as black hole shadows. In this study, we aim to investigate the behavior of the shadow shapes of higher-dimensional charged black hole solutions including asymptotically locally flat (ALF) and asymptotically locally AdS (ALAdS) in Einstein-Horndeski-Maxwell (EHM) gravitational theory. We utilize the Hamilton-Jacobi method to find photon orbits around these black holes as well as the Carter approach to formulate the geodesic equations. We examine how extra dimensions, negative cosmological constant, electric charge, and coupling constants of the EHM gravity affect the shadow size of the black hole. Then, we constrain these parameters by comparing the shadow radius of these black holes with the shadow size of M87* supermassive black hole captured by the Event Horizon Telescope (EHT) collaborations. We discover that generally the presence of extra dimensions within the EHM gravity results in reducing the shadow size of higher-dimensional ALF and ALAdS charged black holes, whereas the impact of electric charge on the shadow of these black holes is suppressible....

##### 9.General Proof of the Tolman law

**Authors:**Minghao Xia, Sijie Gao

**Abstract:** Tolman proposed that the proper temper $T$ of a static self-gravitating fluid in thermodynamic equilibrium satisfies the relation $\chi T=constant$, where $\chi$ is the redshift factor of the spacetime. The Tolman law has been proven for radiation in stationary spacetimes and for perfect fluids in stationary, asymototically flat and axisymmetric spacetimes. It is unclear whether the proof can be extended to more general cases. In this paper, we prove that under some reasonable conditions, the Tolman law always holds for a perfect fluid in a stationary spacetime. The key assumption in our proof is that the particle number density $n$ can not be determined by the energy density $\rho$ and pressure $p$ via the equations of state. This is true for many known fluids with the equation of state $p=p(\rho)$. Then, by requiring that the total entropy of the fluid is an extremum for the variation of $n$ with a fixed metric, we prove the Tolman law. In our proof, only the conservations of stress energy and the total particle number are used, and no field equations are involved. Our work suggests that the Tolman law holds for a generic perfect fluid in a stationary spacetime, even beyond general relativity.

##### 1.Parity violations induced black hole scalarizations

**Authors:**Hao-Jie Lin, Tao Zhu, Shao-Jun Zhang, Anzhong Wang

**Abstract:** It is well-known that parity symmetry is broken in the weak interaction but conserved for Einstein's general relativity and Maxwell's electromagnetic theory. Nevertheless, parity symmetry could also be violated in the gravitational/electromagnetic sectors if a fundamental scalar field couples to the parity-violating gravitational/electromagnetic curvature terms. Such parity-violating terms, which flip signs under reversed spatial directions, can inevitably lead to a negative effective mass squared for the scalar field perturbations near nonspherical black holes and thus are expected to trigger tachyonic instability. As illustrative examples, we show that the scalar field coupled to gravitational/electromagnetic Chern-Simons terms near a Kerr-Newmann spacetime can develop tachyonic instabilities, leading to equilibrium scalar field configurations in certain parameter region of black holes. This instability, which is an indication of the black hole scalarization process, can occur in a broad class of nonspherical black holes and parity-violating theories.

##### 2.Stringy Running Vacuum Model and current Tensions in Cosmology

**Authors:**Adrià Gómez-Valent, Nick E. Mavromatos, Joan Solà Peracaula

**Abstract:** We discuss the potential alleviation of both the Hubble and the growth of galactic structure data tensions observed in the current epoch of Cosmology in the context of the so-called Stringy Running Vacuum Model (RVM) of Cosmology. This is a gravitational field theory coupled to matter, which, at early eras, contains gravitational (Chern-Simons (CS) type) anomalies and torsion, arising from the fundamental degrees of freedom of the massless gravitational multiplet of an underlying microscopic string theory. The model leads to RVM type inflation without external inflatons, arising from the quartic powers of the Hubble parameter that characterise the vacuum energy density due to primordial-gravitational-wave-induced anomaly CS condensates, and dominate the inflationary era. In modern eras, of relevance to this work, the gravitational anomalies are cancelled by chiral matter, generated at the end of the RVM inflationary era, but cosmic radiation and other matter fields are still responsible for a RVM energy density with terms exhibiting a quadratic-power-of-Hubble-parameter dependence, but also products of the latter with logarithmic $H$-dependencies, arising from potential quantum-gravity and quantum-matter loop effects. In this work, such terms are examined phenomenologically from the point of view of the potential alleviation of the aforementioned current tensions in Cosmology. Using standard information criteria, we find that these tensions can be substantially alleviated in a way consistent not only with the data, but also with the underlying microscopic theory predictions, associated with the primordial dynamical breaking of supergravity that characterise a pre-RVM-inflationary phase of the model.

##### 3.Multipole moments of a charged rotating disc of dust in general relativity

**Authors:**David Rumler, Reinhard Meinel

**Abstract:** The gravitational and electromagnetic multipole moments of the charged rotating disc of dust, which is an axisymmetric, stationary solution of the Einstein-Maxwell equations in terms of a post-Newtonian expansion, are calculated and discussed. It turns out that the individual mass, angular momentum, electric and magnetic moments are ordered in the sense that higher moments have a lower absolute value. There is an interesting conjecture stating that the absolute values of all higher multipole moments of a uniformly rotating perfect fluid body are always greater than those of the corresponding Kerr spacetime, which we generalize to include charged bodies. We find that for the charged rotating disc of dust the conjecture holds (within the limits of accuracy of the post-Newtonian expansion).

##### 4.Well-posedness of anisotropic and homogeneous solutions to the Einstein-Boltzmann system with a conformal-gauge singularity

**Authors:**Ho Lee, Ernesto Nungesser, John Stalker, Paul Tod

**Abstract:** We consider the Einstein-Boltzmann system for massless particles in the Bianchi I space-time with scattering cross-sections in a certain range of soft potentials. We assume that the space-time has an initial conformal gauge singularity and show that the initial value problem is well posed with data given at the singularity. This is understood by considering conformally rescaled equations. The Einstein equations become a system of singular ordinary differential equations, for which we establish an existence theorem which requires several differentiability and eigenvalue conditions on the coefficient functions together with the Fuchsian conditions. The Boltzmann equation is regularized by a suitable choice of time coordinate, but still has singularities in momentum variables. This is resolved by considering singular weights, and the existence is obtained by exploiting singular moment estimates.

##### 5.Topology in thermodynamics of regular black strings with Kaluza-Klein reduction

**Authors:**Tran N. Hung, Cao H. Nam

**Abstract:** We study the topological defects in the thermodynamics of regular black strings (from a four-dimensional perspective) that is symmetric under the double Wick rotation and constructed in the high-dimensional spacetime with an extra dimension compactified on a circle. We observe that the thermodynamic phases of regular black strings can be topologically classified by the positive and negative winding numbers (at the defects) which correspond to the thermodynamically stable and unstable branches. This topological classification implies a phase transition due to the decay of a thermodynamically unstable regular black string to another which is thermodynamically stable. We confirm these topological properties of the thermodynamics of regular black strings by investigating their free energy, heat capacity, and Ruppeiner scalar curvature of the state space. The Ruppeiner scalar curvature of regular black strings is found to be always negative, implying that the interactions among the microstructures of regular black strings are only attractive.

##### 6.Ergodic Concepts for a Self-Organizing Trivalent Spin Network

**Authors:**Christine C. Dantas
Astrophysics Division, INPE, Brazil

**Abstract:** We consider, from a dynamical systems point of view, a frozen, planar trivalent spin network model in Loop Quantum Gravity (LQG) presenting self-organized criticality (SOC). We obtain a partition function for the domains of stability connecting gauge non-invariant avalanches, leading to an entropy formula for the asymptotic SOC state. We use this formalism to obtain the entropy of a $(2+1)$-dimensional (BTZ) black hole, and conjecture that this entropy reduces to the Bekenstein-Hawking entropy law by an appropriate adjustment of a potential function.

##### 7.Coördinate transformations, metrics and black hole features in the collapsed phase of EDT

**Authors:**Jan Smit

**Abstract:** This is a companion article to `Using massless fields for observing black hole features in the collapsed phase of Euclidean dynamical triangulations' [1]. It clarifies a singular co\"{o}rdinate transformation of an $SO(4)$ invariant metric to the usual spherical co\"{o}rdinates in which, at an instant of time called zero, the metric takes the form of a black hole with an interior. Regular transformations are also studied and found to lead in the zero time limit to the same spatial components of the metric as with the singular one, whereas the time component ends up differently. Components of the Einstein tensor also end up the same. A regular black hole metric is inversely transformed and compared with simulation results in [1].

##### 8.30 years in: Quo vadis generalized uncertainty principle?

**Authors:**Pasquale Bosso, Giuseppe Gaetano Luciano, Luciano Petruzziello, Fabian Wagner

**Abstract:** According to a number of arguments in quantum gravity, both model-dependent and model-independent, Heisenberg's uncertainty principle is modified when approaching the Planck scale. This deformation is attributed to the existence of a minimal length. The ensuing models have found entry into the literature under the term Generalized Uncertainty Principle (GUP). In this work, we discuss several conceptual shortcomings of the underlying framework and critically review recent developments in the field. In particular, we touch upon the issues of relativistic and field theoretical generalizations, the classical limit and the application to composite systems. Furthermore, we comment on subtleties involving the use of heuristic arguments instead of explicit calculations. Finally, we present an extensive list of constraints on the model parameter $\beta$, classifying them on the basis of the degree of rigour in their derivation and reconsidering the ones subject to problems associated with composites.

##### 9.A reduced phase space quantisation of a model in Algebraic Quantum Gravity with polarised $T^3$ Gowdy symmetry

**Authors:**Kristina Giesel, Andreas Leitherer, David Winnekens

**Abstract:** We consider a reduced phase space quantisation of a model with $T^3$ Gowdy symmetry in which gravity has been coupled to Gaussian dust. We complete the quantisation programme in reduced loop quantum gravity (LQG) as well as algebraic quantum gravity (AQG) and derive a Schr\"odinger-like equation with a physical Hamiltonian operator encoding the dynamics. Due to the classical symmetries of the physical Hamiltonian, the operators are quantised in a graph-preserving way in both cases -- a difference to former models available in the literature. As a first step towards applications of the model in AQG, we consider an ansatz that we use to first construct zero volume states as specific solutions of the Schr\"odiger-like equation. We then also find states with a vanishing action of the Euclidean part of the physical Hamiltonian and investigate the degeneracies these states experience via the action of the Lorentzian part of the physical Hamiltonian. The results presented here can be taken as a starting point for deriving effective models as well as analysing the dynamics numerically in future work.

##### 10.Cosmic Energy Density: Particles, Fields and the Vacuum

**Authors:**Cristian Armendariz-Picon, Alberto Diez-Tejedor

**Abstract:** We revisit the cosmic evolution of the energy density of a quantized free scalar field and assess under what conditions the particle production and classical field approximations reproduce its correct value. Because the unrenormalized energy-momentum tensor diverges in the ultraviolet, it is necessary to frame our discussion within an appropriate regularization and renormalization scheme. Pauli-Villars avoids some of the drawbacks of adiabatic subtraction and dimensional regularization and is particularly convenient in this context. In some cases, we can predict the evolution of the energy density irrespectively of the quantum state of the field modes. To further illustrate our results we focus however on the {\it in} vacuum, the preferred quantum state singled out by inflation, and explore to what extent the latter determines the subsequent evolution of the energy density regardless of the unknown details of reheating. We contrast this discussion with examples of transitions to radiation domination that avoid some of the problems of the one commonly studied in the literature, and point out some instances in which the particle production or the classical field approximations lead to the incorrect energy density. Along the way, we also elaborate on the connection of our analysis to dynamical dark energy models and axion-like dark matter candidates.

##### 11.Analytic imaging formation analysis for Dark Matter halos: geometric ray tracing and caustics using the gravitational refraction law

**Authors:**Omar de J. Cabrera-Rosas, Tonatiuh Matos

**Abstract:** One of the most challenging open questions in physics today is discovering the nature of dark matter. In this work we study the imaging formation in dark matter (DM) halos due to an external light source using some DM profiles for comparison with astronomical observations. Approaching these models on a small scale, we analyze the images generated on the lens plane by obtaining the analytical scaled surface mass densities $\Sigma_{*}(x)$ and their corresponding deflection angles $\alpha_{*}(x)$, for later applying a method for ray tracing using the gravitational refraction law. The method is able to locate the positions of the images on the lens plane, by mapping fringes that represent possible sources (such as other galaxies), placed on the source plane. The regions where the strong lensing occurs for each profile, are determined by fixing the $\lambda$ parameter that establishes the ray tracing process. It is shown that the presence of Einstein rings generated by each profile is directly related with the central branch of the caustic. This method gives us a possible alternative way to distinguish between different DM candidates by observing imaging from external sources.

##### 1.Stable photon orbits in stationary axisymmetric spacetimes with an electromagnetic field and a cosmological constant

**Authors:**Jake O. Shipley

**Abstract:** Stable light rings, which are associated with spacetime instabilities, are known to exist in four-dimensional stationary axisymmetric spacetimes that solve the Einstein$\unicode{x2013}$Maxwell equations (so-called electrovacuum solutions, with Faraday tensor $F_{\mu \nu} \neq 0$); however, they are not permitted in pure vacuum ($F_{\mu \nu} = 0$). In this work, we extend this result to spacetimes with a non-zero cosmological constant $\Lambda$. In particular, we demonstrate that stable light rings are permitted in $\Lambda$-electrovacuum ($F_{\mu \nu} \neq 0$, $\Lambda \neq 0$), but ruled out in $\Lambda$-vacuum ($F_{\mu \nu} = 0$, $\Lambda \neq 0$).

##### 2.Dissipative quintessence, and its cosmological implications

**Authors:**Tiberiu Harko

**Abstract:** We consider a generalization of the quintessence type scalar field cosmological models, by adding a multiplicative dissipative term in the scalar field Lagrangian, which is represented in an exponential form. The generalized dissipative Klein-Gordon equation is obtained from the variational principle in a covariant form. The energy-momentum tensor of the dissipative scalar field is also obtained from the dissipative Lagrangian. The generalized Friedmann equations in the presence of the dissipative scalar field are obtained for a specific form of dissipation, with the dissipation exponent represented as the time integral of the product of the Hubble function, and of a function describing the dissipative properties of the scalar field. Several cosmological models, corresponding to different choices of the dissipation function, and of the scalar field potential, are considered in detail. The evolutions of the basic cosmological parameters (Hubble function, deceleration parameter etc.) are investigated by using both analytical and numerical techniques. A comparison with the observational data for the Hubble function, and with the predictions of the standard $\Lambda$CDM paradigm is also presented for each dissipative scalar field model. In the large time limit the model describes an accelerating Universe, with the effective negative pressure induced by the dissipative effects associated to the scalar field. Accelerated expansion in the absence of the scalar field potential is also possible, with the kinetic term dominating the expansionary evolution. The dissipative scalar field models describe well the observational data, with the free parameters of the model obtained by a trial and error method. The obtained results show that the dissipative scalar field model offers an effective dynamical possibility for explaining the recent cosmological observational data.

##### 3.Imprints of Einstein-Maxwell dilaton-axion gravity in the observed shadows of Sgr A* and M87*

**Authors:**Siddharth Kumar Sahoo, Neeraj Yadav, Indrani Banerjee

**Abstract:** Einstein-Maxwell dilaton-axion (EMDA) gravity provides a simple framework to investigate the signatures of string theory. The axion and the dilaton fields arising in EMDA gravity have important implications in inflationary cosmology and in addressing the late time acceleration of the universe. It is therefore instructive to explore the implications of such a model in explaining the astrophysical observations. In this work we explore the role of EMDA gravity in explaining the observed shadows of black holes (M87* and Sgr A*) released by the Event Horizon Telescope (EHT) collaboration. The Kerr-Sen metric represents the exact, stationary and axisymmetric black hole solution of EMDA gravity. Such a black hole is characterized by the angular momentum $a$ acquired from the axionic field and the dilatonic charge $r_2$ arising from string compactifications. We study the role of spin and the dilaton charge in modifying the shape and size of the black hole shadow. We note that black holes with larger dilaton charge cast a smaller shadow. We investigate the consequences of such a result in addressing the EHT observations of M87* and Sgr A*. Our analysis reveals that the shadow of M87* exhibits a preference towards the Kerr scenario. However, when 10% offset in the shadow diameter is considered, $0.1\lesssim r_2\lesssim 0.3$ is observationally favored within 1-$\sigma$. The shadow of Sgr A* on the other hand shows a preference towards the Kerr-Sen scenario since the central value of its shadow can be better explained by a non-zero dilaton charge $0.1 \lesssim r_2 \lesssim 0.4$. However, when the 1-$\sigma$ interval is considered the Kerr scenario is included. We discuss the implications of our results.

##### 4.Light rings and shadows of rotating black holes in the semiclassical gravity with trace anomaly

**Authors:**Zhenyu Zhang, Yehui Hou, Minyong Guo, Bin Chen

**Abstract:** In a recent work by Fernandes [arXiv:2305.10382], an exact stationary and axisymmetric solution was discovered in semiclassical gravity with type-A trace anomaly, identified as a quantum-corrected version of the Kerr black hole. This discovery presents exciting research opportunities for observing non-circular spacetimes. In this study, we explore the light rings and shadow of this black hole solution. Our investigation reveals that there exist prograde and retrograde normal light rings, whose radii increase monotonically with the coupling parameter $\alpha$. We also observe that when $\alpha$ is negative, the shadow area for the quantum-corrected black hole is smaller than that of the Kerr black hole, whereas when $\alpha$ is positive, the area is larger. Furthermore, the NHEKline for nearly extreme black hole disappears when $\alpha$ is greater than zero, while it appears for negative $\alpha$, even if the spin is not too high. Such line sinks in the middle part when $|\alpha|$ is relatively large if $\alpha$ is less than zero.

##### 5.Accelerating Kaluza-Klein Universe in Modified Theory of Gravitation

**Authors:**S. D. Katore, S. P. Hatkar, D. P. Tadas

**Abstract:** The purpose of this paper is to study the Kaluza-Klein universe in the context of the $f(R,T)$ gravity theory using magnetized strange quark matter (MSQM). To obtain exact solutions of field equations, we assume two types of volumetric expansion: power law and exponential law volumetric expansions. The violation of energy conditions has been studied. The physical and geometrical properties of the examined model have also been investigated thoroughly. Keywords: Kaluza-Klein metric, Magnetized Strange Quark Matter, Power and Exponential law, $f(R,T)$ gravity.

##### 6.On the stability and deformability of top stars

**Authors:**Massimo Bianchi, Giorgio Di Russo, Alfredo Grillo, Jose Francisco Morales, Giuseppe Sudano

**Abstract:** Topological stars, or top stars for brevity, are smooth horizonless static solutions of Einstein-Maxwell theory in 5-d that reduce to spherically symmetric solutions of Einstein-Maxwell-Dilaton theory in 4-d. We study linear scalar perturbations of top stars and argue for their stability and deformability. We tackle the problem with different techniques including WKB approximation, numerical analysis, Breit-Wigner resonance method and quantum Seiberg-Witten curves. We identify three classes of quasi-normal modes corresponding to prompt-ring down modes, long-lived meta-stable modes and what we dub `blind' modes. All mode frequencies we find have negative imaginary parts, thus suggesting linear stability of top stars. Moreover we determine the tidal Love and dissipation numbers encoding the response to tidal deformations and, similarly to black holes, we find zero value in the static limit but, contrary to black holes, we find non-trivial dynamical Love numbers and vanishing dissipative effects at linear order. For the sake of illustration in a simpler context, we also consider a toy model with a piece-wise constant potential and a centrifugal barrier that captures most of the above features in a qualitative fashion.

##### 7.Recent results from continuous gravitational wave searches using data from LIGO/Virgo/KAGRA's third observing run

**Authors:**Andrew L. Miller

**Abstract:** The third observing run of advanced LIGO, Virgo and KAGRA brought unprecedented sensitivity towards a variety of quasi-monochromatic, persistent gravitational-wave signals. Continuous waves allow us to probe not just the existence of canonical asymmetrically rotating neutron stars, but also different forms of dark matter, thus showing the wide-ranging astrophysical implications of using a relatively simple signal model. I will describe the major results from the numerous continuous-wave searches that were performed in O3, both inside and outside the LIGO/Virgo/KAGRA collaborations, and show how impactful to multi-messenger physics that they have been.

##### 8.A vacuum solution of modified Einstein equations based on fractional calculus

**Authors:**A. Di Teodoro, E. Contreras

**Abstract:** In this work, we construct a modified version of the Einstein field equations for a vacuum and spherically symmetric spacetime in terms of the Riemann-Louville fractional derivative. The main difference between our approach and other works is that we ensure that both the classical differential equations and the classical solutions are exactly recovered in the limit when the fractional parameter is turned off. We assume that the fractional equations are valid inside and near the horizon radius and match the classical solution at the horizon. Our approach resembles the Herrera--Witten strategy shown in Adv.High Energy Phys. 2018 (2018) 3839103, where the authors constructed an alternative black hole solution by assuming that inside the horizon the spacetime is hyperbolically symmetric and matches the classical spherically symmetric exterior solution at one point at the horizon. We obtain that, depending on the value of the fractional parameter, the solutions can be interpreted as a regular black hole or a gravatar. As a final step, we compute the fractional curvature scalars and show that the solution is regular everywhere inside the horizon.

##### 9.The comoving curvature perturbation in Jordan and Einstein frames

**Authors:**José Jaime Terente Díaz, Mindaugas Karčiauskas

**Abstract:** In the context of $F(\phi)R$ models of gravity, the conformal invariance of the curvature perturbation on the uniform-field slicings has been already demonstrated in several publications. In this work, we study the conformal invariance of the curvature perturbation defined on hypersurfaces that are comoving with an effective fluid. We derive the comoving curvature perturbation in each conformal frame and relate both. It is shown that the conformal invariance of this gauge-invariant curvature perturbation does not always hold, and the analysis on superhorizon and subhorizon scales is performed in the slow-roll regime of inflation. We find that the comoving curvature perturbation is conformally invariant on superhorizon scales but the same cannot be concluded on the subhorizon regime.

##### 10.Accuracy of the slow-rotation approximation for black holes in modified gravity in light of astrophysical observables

**Authors:**Pablo A. Cano, Alexander Deich, Nicolás Yunes

**Abstract:** Near-future, space-based, radio- and gravitational-wave interferometry missions will enable us to rigorously test whether the Kerr solution of general relativity accurately describes astrophysical black holes, or if it requires some kind of modification. At the same time, recent work has greatly improved our understanding of theories of gravity that modify the Einstein-Hilbert action with terms quadratic in the curvature, allowing us to calculate black hole solutions to (essentially) arbitrary order in a slow-rotation expansion. Observational constraints of such quadratic gravity theories require the calculation of observables that are robust against the expansion order of the black hole solution used. We carry out such a study here and determine the accuracy with respect to expansion order of ten observables associated with the spacetime outside a rotating black hole in two quadratic theories of gravity, dynamical-Chern-Simons and scalar-Gauss-Bonnet gravity. We find that for all but the most rapidly rotating black holes, only about the first eight terms in the spin expansion are necessary to achieve an accuracy that is better than the statistical uncertainties of current and future missions.

##### 11.Charged spinning and magnetized test particles orbiting quantum improved charged black holes

**Authors:**Jose Miguel Ladino, Carlos A. Benavides-Gallego, Eduard Larrañaga, Javlon Rayimbaev, Farrux Abdulxamidov

**Abstract:** In the present work, we aimed to investigate the dynamics of spinning charged and magnetized test particles around both electrically and magnetically charged quantum-improved black holes. We derive the equations of motion for charged spinning test particles using the Mathisson-Papapetrou-Dixon equations with the Lorentz coupling term. The radius of innermost stable circular orbits (ISCOs), specific angular momentum, and energy for charged spinless, uncharged spinning, and charged spinning test particles around the charged and non-charged quantum-improved black holes are analyzed separately. We found that the quantum parameter increases the maximum spin value, $s_\text{max}$, which leads to the nonphysical motion (superluminal motion) of the charged spinning test particle, whereas the black hole charge decreases its value. We also found that, in contrast to the Reissner Nordstr\"om black hole, spinning charged test particles in the quantum-improved charged black hole have higher $s_\text{max}$; moreover, positively charged spinning particles can have higher values of $s_\text{max}$ near the extreme black hole cases when compared with uncharged spinning particles. Finally, we investigate the magnetized test particle's dynamics around a quantum-improved magnetically charged black hole in Quantum Einstein Gravity using the Hamilton-Jacobi equation. We show that the presence of $\omega$ increases the maximum value of the effective potential and decreases the minimum energy and angular momentum of magnetized particles at their circular orbits. We found an upper constraint in the black hole charge at the ISCO.

##### 1.Thermal analysis and Joule-Thomson expansion of black hole exhibiting metric-affine gravity

**Authors:**Muhammad Yasir, Xia Tiecheng, Faisal Javed, G. Mustafa

**Abstract:** This study examines a recently hypothesized black hole, which is a perfect solution of metric-affine gravity with a positive cosmological constant, and its thermodynamic features as well as the Joule-Thomson expansion. We develop some thermodynamical quantities, such as volume, Gibbs free energy, and heat capacity, using the entropy and Hawking temperature. We also examine the first law of thermodynamics and thermal fluctuations, which might eliminate certain black hole instabilities. In this regard, a phase transition from unstable to stable is conceivable when the first law order corrections are present. Besides that, we study the efficiency of this system as a heat engine and the effect of metric-affine gravity for physical parameters $q_e$, $q_m$, $\kappa_{\mathrm{s}}$, $\kappa_{\mathrm{d}}$ and $\kappa_{\mathrm{sh}}$. Further, we study the Joule-Thomson coefficient, and the inversion temperature and also observed the isenthalpic curves in the $T_i -P_i$ plane. In metric-affine gravity, a comparison is made between the Van der Waals fluid and the black hole to study their similarities and differences.

##### 2.Can electromagnetic charge inhabit in Rastall gravity?

**Authors:**Bobir Toshmatov, Zdeněk Stuchlík, Bobomurat Ahmedov

**Abstract:** One of the eminent generalizations of theory of general relativity is the Rastall gravity which was {constructed} based on the assumption of the non-conserved energy-momentum tensor of the matter field. Despite in the literature several solutions of black holes in the Rastall gravity coupled to the electromagnetic field have been presented, in the current paper we argue that the Rastall gravity with non-conserved energy-momentum tensor (with $\lambda\neq0$ and $R\neq0$) cannot couple to the electrodynamics, i.e., the electromagnetically charged black hole solution cannot be obtained in this case. This statement is adequate for both linear and nonlinear electrodynamics with the electric, magnetic, or dyonic charges coupled to the Rastall gravity.

##### 3.Modified Friedmann Equations from Maxwell-Weyl Gauge Theory

**Authors:**Salih Kibaroğlu

**Abstract:** This study investigates the possibility of a homogeneous and isotropic cosmological solution within the context of the Maxwell-Weyl gauge theory of gravity. To achieve this, we utilize the Einstein-Yang-Mills theory as an analogy and represent the Maxwell gauge field in terms of two time-dependent scalar fields. Then, we present the modified Friedmann equations, which incorporate the contributions of the Maxwell gauge field, as well as the effective cosmological constant, which is a function of the Dirac scalar field.

##### 4.Spins of primordial black holes formed with a soft equation of state

**Authors:**Daiki Saito, Tomohiro Harada, Yasutaka Koga, Chul-Moon Yoo

**Abstract:** We investigate the probability distribution of the spins of primordial black holes (PBHs) formed in the universe dominated by a perfect fluid with the linear equation of state $p=w\rho$, where $p$ and $\rho$ are the pressure and energy density of the fluid, respectively. We particularly focus on the parameter region $0<w\leq 1/3$ since the larger value of the spin is expected for the softer equation of state than that of the radiation fluid ($w=1/3$). The angular momentum inside the collapsing region is estimated based on the linear perturbation equation at the turn-around time which we define as the time when the linear velocity perturbation in the conformal Newtonian gauge takes the minimum value. The probability distribution is derived based on the peak theory with the Gaussian curvature perturbation. We find that the root mean square of the non-dimensional Kerr parameter $\sqrt{\langle a_{*}^2\rangle}$ is approximately proportional to $(M/M_{H})^{-1/3}(6w)^{-(1+2w)/(1+3w)}$, where $M$ and $M_{H}$ are the mass of the PBH and the horizon mass at the horizon entry, respectively. Therefore the typical value of the spin parameter decreases with the value of $w$. We also evaluate the mass and spin distribution $P(a_{*}, M)$, taking account of the critical phenomena. We find that, while the spin is mostly distributed in the range of $10^{-3.9}\leq a_{*}\leq 10^{-1.8}$ for the radiation-dominated universe, the peak of the spin distribution is shifted to the larger range $10^{-3.0}\leq a_{*}\leq 10^{-0.7}$ for $w=10^{-3}$.

##### 5.Probing high frequency gravitational waves with pulsars

**Authors:**Asuka Ito, Kazunori Kohri, Kazunori Nakayama

**Abstract:** We study graviton-photon conversion in magnetosphere of a pulsar and explore the possibility of detecting high frequency gravitational waves with pulsar observations. It is shown that conversion of one polarization mode of photons can be enhanced significantly due to strong magnetic fields around a pulsar. We also constrain stochastic gravitational waves in frequency range of $10^{8}-10^{9}\,$Hz and $10^{13}-10^{27}\,$Hz by using data of observations of the Crab pulsar and the Geminga pulsar. Our method widely fills the gap among existing high frequency gravitational wave experiments and boosts the frequency frontier in gravitational wave observations.

##### 6.Kinematic topologies of black holes

**Authors:**Jiayu Yin, Jie Jiang, Ming Zhang

**Abstract:** We investigate the kinematic topologies of light rings (LRs) and massive particle rings (PRs) encircling spherical and axisymmetric black holes. Our results demonstrate that the global topology number of LRs is consistently -1, independent of the spacetime background's asymptotic property. Additionally, we show that the global topology of PRs varies, with a value of 0 in asymptotically flat and Anti-de Sitter spacetime but -1 in asymptotic de Sitter spacetime.

##### 7.Bayesian Time Delay Interferometry for Orbiting LISA: Accounting for the Time Dependence of Spacecraft Separations

**Authors:**Jessica Page, Tyson Littenberg

**Abstract:** Previous work demonstrated effective laser frequency noise (LFN) suppression for Laser Interferometer Space Antenna (LISA) data from raw phasemeter measurements using a Markov Chain Monte Carlo (MCMC) algorithm with fractional delay interpolation (FDI) techniques to estimate the spacecraft separation parameters required for time-delay interferometry (TDI) under the assumption of a rigidly rotating LISA configuration. Including TDI parameters in the LISA data model as part of a global fit analysis pipeline enables gravitational wave inferences to be marginalized over uncertainty in the spacecraft separations. Here we extend the algorithm's capability to perform data-driven TDI on LISA in Keplerian orbits, which introduce a time-dependence in the arm-length parameters and at least $\mathcal{O}$(M) times greater computational cost since the filter must be applied for every sample in the time series of sample size M. We find feasibility of arm-length estimation on $\sim$day-long time scales by using a novel Taylor-expanded version of the fractional delay interpolation filter that allows half of the filter computation to be calculated and stored before MCMC iterations and requires shorter filter lengths than previously reported. We demonstrate LFN suppression for orbiting LISA using accurate arm-length estimates parameterized by Keplerian orbital parameters under the assumption of unperturbed analytical Keplerian orbits, and explore the potential extension of these methods to arbitrary numerical orbits.

##### 1.Petrov classification of analogue spacetimes

**Authors:**Sang-Shin Baak, Satadal Datta, Uwe R. Fischer

**Abstract:** In an effort to invariantly characterize the conformal curvature of analogue spacetimes built from a nonrelativistic background, we determine the Petrov type of a variety of lab fluid geometries. Starting from the simplest examples, we increase the complexity of the background, and thereby determine how the lab fluid symmetry affects the corresponding Petrov type in the analogue spacetime realm of the sound waves. We find that for more complex flows isolated hypersurfaces develop, which are of a Petrov type differing from that of the surrounding fluid.

##### 2.Blandford-Znajek Process in Einsteinian Cubic Gravity

**Authors:**Jun Peng, Xing-Hui Feng

**Abstract:** In this paper, we investigate the Blandford-Znajek (BZ) process within the framework of Einsteinian cubic gravity (ECG). To analytically study the BZ process using the split monopole configuration, we construct a slowly rotating black hole in ECG up to cubic order in small spin, considering the leading order in small coupling constant of higher curvature terms. By deriving the magnetosphere solution around the black hole, we determine the BZ power up to the second relative order in spin. The BZ power is modified by the coupling constant compared to Kerr black hole. Although the general nature of the BZ process in ECG remains unchanged at the leading order in spin, the coupling constant introduces modification at the second relative order in spin. Therefore, we anticipate that it is feasible to discern general relativity from higher derivative gravities by examining the BZ power in rapidly rotating black holes.

##### 3.Prediction for the interferometric shape of the first black hole photon ring

**Authors:**Alejandro Cárdenas-Avendaño, Alexandru Lupsasca

**Abstract:** Black hole images are theoretically predicted (under mild astrophysical assumptions) to display a stack of lensed "photon rings" that carry information about the underlying spacetime geometry. Despite vigorous efforts, no such ring has been observationally resolved thus far. However, planning is now actively under way for space missions targeting the first (and possibly the second) photon rings of the supermassive black holes M87* and Sgr A*. In this work, we study interferometric photon ring signatures in time-averaged images of Kerr black holes surrounded by different astrophysical profiles. We focus on the first, most easily accessible photon ring, which has a larger width-to-diameter ratio than subsequent rings and whose image consequently lacks a sharply defined diameter. Nonetheless, we show that it does admit a precise angle-dependent diameter in visibility space, for which the Kerr metric predicts a specific functional form that tracks the critical curve. We find that a measurement of this interferometric ring diameter is possible for most astrophysical profiles, paving the way for precision tests of strong-field general relativity via near-future observations of the first photon ring.

##### 4.Positivity Conditions for Generalised Schwarzschild Space-Times

**Authors:**A. D'Alise, G. Fabiano, D. Frattulillo, S. Hohenegger, D. Iacobacci, F. Pezzella, F. Sannino

**Abstract:** We analyse the impact of positivity conditions on static spherically symmetric deformations of the Schwarzschild space-time. The metric is taken to satisfy, at least asymptotically, the Einstein equation in the presence of a non-trivial stress-energy tensor, on which we impose various physicality conditions. We systematically study and compare the impact of these conditions on the space-time deformations. The universal nature of our findings applies to both classical and quantum metric deformations with and without event horizons. We further discuss minimal realisations of the asymptotic stress energy tensor in terms of physical fields. Finally, we illustrate our results by discussing concrete models of quantum black holes.

##### 5.Hamiltonian charges on light cones for linear field theories on (A)dS backgrounds

**Authors:**Piotr T. Chruściel, Tomasz Smołka

**Abstract:** We analyse the Noether charges for scalar and Maxwell fields on light cones on a de Sitter, Minkowski, and anti-de Sitter backgrounds. Somewhat surprisingly, under natural asymptotic conditions all charges for the Maxwell fields on both the de Sitter and anti-de Sitter backgrounds are finite. On the other hand, one needs to renormalise the charges for the conformally-covariant scalar field when the cosmological constant does not vanish. In both cases well-defined renormalised charges, with well-defined fluxes, are obtained. Again surprisingly, a Hamiltonian analysis of a suitably rescaled scalar field leads to finite charges, without the need to renormalise. Last but not least, we indicate natural phase spaces where the Poisson algebra of charges is well defined.

##### 6.Traversable wormholes in bi-metric gravity

**Authors:**Mostafizur Rahman, Anjan A Sen, Sunil Singh Bohra

**Abstract:** The ghost-free bi-metric gravity theory is a viable theory of gravity that explores the interaction between a massless and a massive graviton and can be described in terms of two dynamical metrics. In this paper, we present an exact static, spherically symmetric vacuum solution within this theory. The solution is spatially Schwarzschild-de Sitter, with the value of the cosmological constant determined by the graviton mass and the interaction parameters of the theory. Notably, for specific parameter ranges, the solution represents a traversable Lorentzian wormhole that violates the weak energy condition near its throat. Furthermore, we have investigated the evolution of scalar and electromagnetic fields in this wormhole spacetime and observed the presence of arbitrarily long-lived quasi-resonant modes in the quasinormal spectrum.

##### 7.The accelerated expansion in $F(G,T_{μν}T^{μν})$ gravity

**Authors:**Mihai Marciu, Dana Maria Ioan

**Abstract:** In the present manuscript the basic Einstein--Hilbert cosmological model is extended, by adding a new functional $F(G, T_{\mu\nu}T^{\mu\nu})$ in the fundamental action, encoding specific geometrical effects due to a nontrivial coupling with the Gauss-Bonnet invariant ($G$), and the energy--momentum squared term ($T_{\mu\nu}T^{\mu\nu}$). After obtaining the corresponding gravitational field equations for the specific decomposition where $F(G, T_{\mu\nu}T^{\mu\nu})=f(G)+g(T_{\mu\nu}T^{\mu\nu})$, we have explored the physical features of the cosmological model by considering the linear stability theory, an important analytical tool in the cosmological theory which can reveal the dynamical characteristics of the phase space. The analytical exploration of the corresponding phase space structure revealed that the present model can represent a viable dark energy model, with various stationary points where the effective equation of state corresponds to a de--Sitter epoch, possible explaining the early and late time acceleration of the Universe.

##### 8.Vacuum defect wormholes and a mirror world

**Authors:**F. R. Klinkhamer

**Abstract:** We have recently obtained a smooth vacuum-wormhole solution of the first-order equations of general relativity. Here, we present the corresponding multiple vacuum-wormhole solution. Assuming that our world is essentially Minkowski spacetime with a large number of these vacuum defect wormholes inserted, there is then another flat spacetime with opposite spatial orientation, which may be called a "mirror" world. We briefly discuss some phenomenological aspects and point out that there will be no significant vacuum-Cherenkov radiation in our world, so that ultrahigh-energy cosmic rays do not constrain the typical sizes and separations of the wormhole mouths (different from the constraints obtained for a single Minkowski spacetime with similar defects).

##### 1.Exact conditions for antiUnruh effect in (1+1)-dimensional spacetime

**Authors:**Dawei Wu, Ji-chong Yang, Yu Shi

**Abstract:** Exact conditions for antiUnruh effect in (1+1)-dimensional spacetime are obtained. For detectors with Gaussian switching functions, the analytic results are similar to previous ones, indicating that antiUnruh effect occurs when the energy gap matches the characteristic time scale. However, this conclusion does not hold for detectors with square wave switching functions, in which case the condition turns out to depend on both the energy gap and the characteristic time scale in some nontrivial way. We also show analytically that there is no antiUnruh effect for detectors with Gaussian switching functions in (3+1)-dimensional spacetime.

##### 2.Interior spacetimes sourced by stationary differentially rotating irrotational cylindrical fluids. Perfect fluids

**Authors:**Marie-Noëlle Célérier

**Abstract:** In a recent series of papers new exact analytical solutions of the Einstein equations representing interior spacetimes sourced by stationary rigidly rotating cylinders of different kinds of fluids have been displayed, C\'el\'erier, Phys. Rev. D 104, 064040 (2021), J. Math. Phys. 64, 022501 (2023), J. Math. Phys. 64, 032501 (2023), J. Math. Phys. 64, 042501 (2023), arXiv:2208.06899 [gr-qc]. This work is currently being extended to the cases of differentially rotating irrotational fluids. The results are presented in a new series of papers considering in turn the same three anisotropic pressure cases, as well as a perfect fluid source. Here, the perfect fluid case is considered, and different classes are identified as directly issuing from the field equations. Among them, an explicit analytical set of solutions is selected as displaying perfect fluid spacetimes. Its mathematical and physical properties are analyzed. Its matching to an exterior Lewis-Weyl vacuum and the conditions for avoiding an angular deficit are discussed.

##### 3.Cosmic string bursts in LISA

**Authors:**Pierre Auclair, Stanislav Babak, Hippolyte Quelquejay Leclere, Danièle A. Steer

**Abstract:** Cosmic string cusps are sources of short-lived, linearly polarised gravitational wave bursts which can be searched for in gravitational wave detectors. We assess the capability of LISA to detect these bursts using the latest LISA configuration and operational assumptions. For such short bursts, we verify that LISA can be considered as ``frozen", namely that one can neglect LISA's orbital motion. We consider two models for the network of cosmic string loops, and estimate that LISA should be able to detect 1-3 bursts per year assuming a string tension $G\mu \approx 10^{-11} - 10^{-10.5}$ and detection threshold $\rm{SNR} \ge 20$. Non-detection of these bursts would constrain the string tension to $G\mu\lesssim 10^{-11}$ for both models.

##### 4.Black holes of the Vaidya type with flat and (A)dS asymptotics as point particles

**Authors:**A. N. Petrov

**Abstract:** A presentation of the Vaidya type Schwarzschild-like black holes with flat, AdS and dS asymptotics in 4-dimensional general relativity in the form of a pointlike mass is given. True singularities are described by making the use of the Dirac $\delta$-function in a non-contradictory way. The results essentially generalize previous derivations where the usual Schwarzschild black hole solution is represented in the form of a point particle. The field-theoretical formulation of general relativity, which is equivalent to its standard geometrical formulation, is applied as an alternative mathematical formalism. Then perturbations on a given background are considered as dynamical fields propagating in a given (fixed) spacetime. The energy (mass) distribution of such field configurations is just represented as a point mass. The new derivation of black holes' structure can be useful in explaining and understanding their features and can be applied in calculations with black hole models.

##### 5.Some remarks on Hayward black hole with a cloud of strings

**Authors:**F. F. Nascimentoa, V. B. Bezerrab, J. M. Toledo

**Abstract:** We obtain the metric corresponding to the Hayward black hole spacetime surrounded by a cloud of strings and investigate the role played by this cloud on the horizons, geodesics, effective potential and thermodynamics. We compare the obtained results with the ones of the literature, corresponding to the Hayward black hole, when the cloud of strings is absent. Also, the question related to its nature, with respect to regularity, in this scenario, is examined.

##### 6.Matter-gravity entanglement entropy and the second law for black holes

**Authors:**Bernard S. Kay
York

**Abstract:** Hawking showed that a black hole formed by collapse will emit radiation and eventually disappear. We address the challenge to define an objective notion of physical entropy which increases throughout this process in a way consistent with unitarity. We have suggested that (instead of coarse-grained entropy) physical entropy is matter-gravity entanglement entropy and that this may offer an explanation of entropy increase both for the black hole collapse and evaporation system and also for other closed unitarily evolving systems. For this to work, the matter-gravity entanglement entropy of the late-time state of black hole evaporation would have to be larger than the entropy of the freshly formed black hole. We argue that this may possibly be the case due to (usually neglected) photon-graviton interactions.

##### 7.Thermodynamics as a tool for (quantum) gravitational dynamics

**Authors:**Ana Alonso-Serrano, Marek Liška

**Abstract:** The thermodynamics of local causal horizons has been shown to imply gravitational dynamics. In this essay, we discuss the principles underlying this observation, and its significance in our understanding of (quantum) gravity. We also show why the local thermodynamic methods cannot by themselves recover general relativity. Instead, they lead to the so-called Weyl transverse gravity. Because of this, local thermodynamic approaches avoid huge vacuum energy contributions to the cosmological constant. They even suggest a possible source for its small observed value. We also outline a way in which thermodynamics allows us to study low energy quantum gravitational effects. We arrive at quantum corrections to the gravitational equations which are suppressed by the Planck length squared.

##### 1.X-Ray Tests of General Relativity with Black Holes

**Authors:**Cosimo Bambi

**Abstract:** General relativity is one of the pillars of modern physics. For decades, the theory has been mainly tested in the weak field regime with experiments in the Solar System and radio observations of binary pulsars. Until 2015, the strong field regime was almost completely unexplored. Thanks to new observational facilities, the situation has dramatically changed in the last few years. Today we have gravitational wave data of the coalesce of stellar-mass compact objects from the LIGO-Virgo-KAGRA Collaboration, images at mm wavelengths of the supermassive black holes in M87$^*$ and SgrA$^*$ from the Event Horizon Telescope Collaboration, and X-ray data of accreting compact objects from a number of X-ray missions. Gravitational wave tests and black hole imaging tests are certainly more popular and are discussed in other articles of this Special Issue. The aim of the present manuscript is to provide a pedagogical review on X-ray tests of general relativity with black holes and to compare this kind of tests with those possible with gravitational wave data and black hole imaging.

##### 2.Poincaré invariance of spinning binary dynamics in the post-Minkowskian Hamiltonian approach

**Authors:**Hojin Lee, Sangmin Lee

**Abstract:** We initiate the construction of the global Poincar\'e algebra generators in the context of the post-Minkowskian Hamiltonian formulation of gravitating binary dynamics in isotropic coordinates that is partly inspired by scattering amplitudes. At the first post-Minkowskian (1PM) order, we write down the Hamiltonian in a form valid in an arbitrary inertial frame. Then we construct the boost generator at the same order which uniquely solves all the equations required by the Poincar\'e algebra. Our results are linear in Newton's constant but exact in velocities and spins, including all spin multiple moments. We also compute the generators of canonical transformations that proves the equivalence between our new generators and the corresponding generators in the ADM coordinates up to the second post-Newtonian (2PN) order.

##### 3.Up-down binaries are unstable and we want to know

**Authors:**Viola De Renzis

**Abstract:** The relativistic spin-precession equations for black-hole binaries have four different equilibrium solutions that correspond to systems where the two individual black hole spins are either aligned or anti-aligned with the orbital angular momentum. Surprisingly, it was demonstrated that only three of these equilibrium solutions are stable. Binary systems in the up-down configuration, where the spin of the heavier (lighter) black hole is co- (counter-) aligned with the orbital angular momentum, might be unstable to small perturbations of the spin directions. After the onset of the up-down instability, that occurs after a specific critical orbital separation $r_\mathrm{UD+}$, the binary becomes unstable to spin precession leading to large misalignment of the spins. In this work, we present a Bayesian procedure based on the Savage-Dickey density ratio to test the up-down origin of gravitational-wave events. We apply this procedure to look for promising candidates among the events detected so far during the first three observing runs performed by LIGO/Virgo.

##### 4.Dark matter condensates as highly nonlocal solitons: instability in the Schwarzschild metric and laboratory analog

**Authors:**Ludovica Dieli, Claudio Conti

**Abstract:** Theories on the bosonic nature of dark matter are a promising alternative to the cold dark matter model. Here we consider a dark matter halo in the state of a Bose-Einstein condensate, subject to the gravitation of a black hole. In the low energy limit, we bring together the general relativity in the Schwarzschild metric and the quantum description of the Bose-Einstein condensate. The model is solvable in the Fermi normal coordinates with the so called highly nonlocal approximation and describes tidal deformations in the condensate wave function. The black hole deforms the localized condensate until the attraction of the compact object overcomes the self-gravitation and destabilizes the solitonic dark matter. Moreover, the model can be implemented as a gravitational analog in the laboratory; the time-dependent potential generated by the galactic black hole can be mimicked by an optical trap acting on a conventional condensate. The results open the way to new laboratory simulators for quantum gravitational effects.

##### 5.Probing the Lorentz Invariance Violation via Gravitational Lensing and Analytical Eigenmodes of Perturbed Slowly Rotating Bumblebee Black Holes

**Authors:**M. Mangut, H. Gürsel, S. Kanzi, İ. Sakallı

**Abstract:** The ability of bumblebee gravity models to explain dark energy, which is the phenomenon responsible for the universe's observed accelerated expansion, is one of their most significant applications. An effect that causes faster expansion can be linked to how much the Lorentz symmetry of our universe is violated. Moreover, since we do not know what generates dark energy, the bumblebee gravity theory seems highly plausible. By utilizing the physical changes happening around a rotating bumblebee black hole (RBBH), we aim to obtain more specific details about the bumblebee black hole's spacetime and our universe. However, as researched in the literature, slow-spinning RBBH (SRBBH) spacetime, which has a higher accuracy, will be considered instead of general RBBH. To this end, we first employ the Rindler--Ishak method (RIM), which enables us to study how light is bent in the vicinity of a gravitational lens. We evaluate the deflection angle of null geodesics in the equatorial plane of the SRBBH spacetime. Then, we use astrophysical data to see the effect of the Lorentz symmetry breaking (LSB) parameter on the bending angle of light for numerous astrophysical stars and black holes. We also acquire the analytical greybody factors (GFs) and quasinormal modes (QNMs) of the SRBBH. Finally, we visualize and discuss the results obtained in the conclusion section.

##### 6.Lie Symmetry Analysis of the Einstein-Maxwell Equations for Quark Stars

**Authors:**Muhammad Al-Zafar Khan, Riven Narain

**Abstract:** We derive the Lie point symmetries for the MIT Bag Model for quark stars in relativistic astrophysics. Four cases of reduction arise; three cases of specific values of the measure of the anisotropy variation, and one general case, which we postulate as a specific relationship between the two gravitational potentials. We demonstrate the applicability of the model by generating two closed form solutions that satisfy the master gravitational equation and we match the interior geometries of the gravitating hyperspheres with the external solution given by the Reissner-Nordstr\"{o}m metric at the stellar boundary. Lastly, we produce a general class of solutions that are attainable for smooth and continuous functions and generate two exact solutions using this model.

##### 7.Primordial black holes from null energy condition violation during inflation

**Authors:**Yong Cai, Mian Zhu, Yun-Song Piao

**Abstract:** The violation of the null energy condition (NEC) is closely related to potential solutions for the cosmological singularity problem and may therefore play a crucial role in the very early universe. We explore a novel approach to generate primordial black holes (PBHs) via the violation of the NEC in a single-field inflationary scenario. In our scenario, the universe transitions from a first slow-roll inflation stage with a Hubble parameter H = Hinf1 to a second slow-roll inflation stage with H = Hinf2 > Hinf1, passing through an intermediate stage of NEC violation. The resulting primordial scalar power spectrum is naturally enhanced by the NEC violation at a certain wavelength. As a result, PBHs with masses and abundances of observational interest can be produced in our scenario. We also examine the phenomenological signatures of scalar-induced gravitational waves (SIGWs). Our work highlights the significance of utilizing a combination of PBHs, SIGWs, and primordial gravitational waves as a powerful probe for exploring the NEC violation during inflation.

##### 8.Cosmological Einstein-Lambda-perfect-fluid solutions with asymptotic dust or radiation equation of state

**Authors:**Helmut Friedrich

**Abstract:** This article introduces the notions of asymptotic dust and asymptotic radiation equations of state. With these non-linear generalizations of the well known dust or (incoherent) radiation equations of state the perfect-fluid equations loose any conformal covariance or privilege. We analyse the conformal field equations induced with these equations of state. It is shown that the Einstein-Lambda-perfect-fluid equations with an asymptotic radiation equation of state allow for large sets of data that develop into solutions which admit smooth conformal boundaries in the future and smooth extensions beyond.

##### 9.Non-interacting String and Holographic Dark Energy Cosmological Models in f(R) Theory of Gravitation

**Authors:**S. P. Hatkar, D. P. Tadas, S. D. Katore

**Abstract:** In this paper, a new class of string and holographic dark energy (HDE) cosmological model in the context of f(R) theory of gravity using the Kasner metric is considered. The exact solution of filed equations are obtained by using the relation between average scale factor and the scalar function f(R). It is observed that the universe is accelerating and expanding. The string phase of the universe is present at early stage of evolution of the universe. The universe is dominated by quintessence type HDE at present. Effect of the curvature function f(R) is also observed on dynamical parameters.

##### 10.Bianchi type $VI_0$ space time domain walls in modified theory of gravitation

**Authors:**S. P. Hatkar, D. P. Tadas, S. D. Katore

**Abstract:** We consider the Bianchi type-$ VI_0 $ space time with domain walls in the framework of modified $f(R,T)$ theory of gravitation. To solve the field equations we assume that shear scalar $(\sigma)$ is proportional to expansion scalar $(\theta)$. We also consider parametrization of equation of state parameter of barotropic fluid and discuss the effect for domain walls. It is observed that the domain wall may behave like dark energy. Some physical parameters are also discussed in details.

##### 11.The Analytical Solutions of Equatorial Geodesic Motion in Kerr Spacetime

**Authors:**Yan Liu, Bing Sun

**Abstract:** In this study, we provide explicit analytical solutions for equatorial timelike geodesics in Kerr spacetime. These solutions capture the characteristics of special geodesics, including the positions and conserved quantities of circular orbits, bound orbits, and deflecting orbits. Specifically, we determine the precise location at which retrograde orbits undergo a transition from counter-rotating to prograde motion due to the strong gravitational effects near the rotating black hole. Interestingly, we observe that for orbits with negative energy, the trajectory remains prograde despite the negative angular momentum. Furthermore, we investigate the intriguing phenomenon of deflecting orbits exhibiting an increased number of revolutions around the black hole as the turning points approaches to each other. Additionally, we find that only prograde marginal deflecting geodesics are capable of traversing through the ergoregion. In summary, our findings present explicit solutions for equatorial timelike geodesics and offer insights into the dynamics of particle motion in the vicinity of a rotating black hole.

##### 12.Gravitational lensing in a topologically charged Eddington-inspired Born-Infeld spacetime

**Authors:**A. R. Soares, R. L. L. Vitória, C. F. S. Pereira

**Abstract:** In the present paper, we study several aspects of gravitational lensing caused by a topologically charged Monopole/Wormhole, both in the weak field limit and in the strong field limit. We calculate the light deflection and then use it to determine the observables, with which one can investigate the existence of these objects through observational tools. We emphasize that the presence of the topological charge produces changes in the observables in relation to the case of General Relativity Ellis-Bronnikov wormhole.

##### 13.Shadows of black holes at cosmological distances in the co-varying physical couplings framework

**Authors:**R. R. Cuzinatto, C. A. M. de Melo, Juliano C. S. Neves

**Abstract:** The co-varying physical couplings (CPC) framework states that physical parameters like the speed of light in vacuum $c$, the Newtonian constant $G$, and the cosmological constant $\Lambda$ could indeed vary with the spacetime coordinates $x^{\mu}$. Here, we assume a temporal variation, that is, $c(t),G(t)$ and $\Lambda(t)$. We show that the McVittie spacetime, a black hole in an expanding universe, is a solution of the CPC framework providing naturally an important parameter of the model. Then, we calculate the shadow angular radius of this black hole at cosmological distances. A black hole shadow in the CPC context could be either larger or smaller than the same shadow in the standard cosmology. It depends on how the set $\{ c,G,\Lambda \}$ varies with time or with the cosmic expansion.

##### 1.Quantum Geometrodynamics Revived I. Classical Constraint Algebra

**Authors:**Thorsten Lang, Susanne Schander

**Abstract:** In this series of papers, we present a set of methods to revive quantum geometrodynamics, which has been buried due to its numerous mathematical and conceptual challenges. In this paper, we introduce the regularization scheme on which we base the subsequent quantization and continuum limit of the theory. Specifically, we constrain the phase space of classical geometrodynamics to piecewise constant fields, resulting in a theory with finitely many degrees of freedom of the spatial metric field. As this representation effectively corresponds to a lattice theory, we can utilize well--known techniques to depict the constraints and their algebra on the lattice. We compute lattice corrections to the constraint algebra and show that they vanish in the continuum limit. This model can now be quantized using the usual methods of finite--dimensional quantum mechanics, as we demonstrate in the following paper. The application of the continuum limit is the subject of a future publication.

##### 2.White dwarf cooling in $f(R,T)$ gravity

**Authors:**Snehasish Bhattacharjee

**Abstract:** In recent times, astounding observations of both over- and under-luminous type Ia supernovae have emerged. These peculiar observations hint not only at surpassing the Chandrasekhar limit but may also suggest potential modifications in the physical attributes of their progenitors, such as their cooling rate. This, in turn, can influence their temporal assessments and provide a compelling explanation for these intriguing observations. In this spirit, we investigate here the cooling process of white dwarfs in $f(R,T)$ gravity with the simplest model $f(R,T) = R + \lambda T$, where $\lambda$ is the model parameter. Our modelling suggests that the cooling timescale of white dwarfs exhibits an inverse relationship with the model parameter $\lambda$, which implies that for identical initial conditions, white dwarfs in $f(R,T)$ gravity cool faster. This further unveils that in the realm of $f(R,T)$ gravity, the energy release rate for white dwarfs increases as $\lambda$ increases. Furthermore, we also report that the luminosity of the white dwarfs also depends on $\lambda$ and an upswing in $\lambda$ leads to an amplification in the luminosity, and consequently a larger white dwarf in general relativity can exhibit comparable luminosity to a smaller white dwarf in $f(R,T)$ gravity.

##### 3.Bounding the mass of ultralight bosonic Dark Matter particles with the motion of the S2 star around Sgr A*

**Authors:**Riccardo Della Monica, Ivan de Martino

**Abstract:** Dark matter is undoubtedly one of the fundamental, albeit unknown, components of the standard cosmological model. The failure to detect WIMPs, the most promising candidate particle for cold dark matter, actually opens the way for the exploration of viable alternatives, of which ultralight bosonic particles with masses $\sim 10^{-21}$ eV represent one of the most encouraging. N-body simulations have shown that such particles form solitonic cores in the innermost parts of virialized galactic halos that are supported by internal quantum pressure on characteristic $\sim$kpc de Broglie scales. In the Galaxy, this halo region can be probed by means of S-stars orbiting the supermassive black hole Sagittarius A* to unveil the presence of such a solitonic core and, ultimately, to bound the boson mass $m_\psi$. Employing a Monte Carlo Markov Chain algorithm, we compare the predicted orbital motion of S2 with publicly available data and set an upper bound $m_\psi \lesssim 3.2\times 10^{-19}$ eV on the boson mass, at 95% confidence level. When combined with other galactic and cosmological probes, our constraints help to reduce the allowed range of the bosonic mass to $(2.0 \lesssim m_\psi \lesssim 32.2)\times 10^{-20}$ eV, at the 95% confidence level, which opens the way to precision measurements of the mass of the ultralight bosonic dark matter.

##### 4.Rotating black holes in semiclassical gravity

**Authors:**Pedro G. S. Fernandes

**Abstract:** We present analytic stationary and axially-symmetric black hole solutions to the semiclassical Einstein equations that are sourced by the trace anomaly. We also find that the same spacetime geometry satisfies the field equations of a subset of Horndeski theories featuring a conformally coupled scalar field. We explore various properties of these solutions, and determine the domain of existence of black holes. These black holes display distinctive features, such as a non-spherically symmetric event horizon and violations of the Kerr bound.

##### 1.Analytic three-dimensional hairy charged black holes and thermodynamics

**Authors:**Supragyan Priyadarshinee, Subhash Mahapatra

**Abstract:** We present and discuss new families of hairy charged black hole solutions in asymptotically anti-de Sitter space in three dimensions. The coupled Einstein-Maxwell-scalar gravity system, that carries the coupling $f(\phi)$ between the scalar and Maxwell fields is solved, and exact hairy black hole solutions are obtained analytically. The hairy solutions are obtained for three different profiles of the coupling function: (i) $f(\phi)=1$, corresponding to no direct coupling between the scalar and Maxwell fields, (ii) $f(\phi)=e^{-\phi}$, and (iii) $f(\phi)=e^{-\phi^2/2}$; corresponding to non-minimal coupling between them. For all these couplings the scalar field and curvature scalars are regular everywhere outside the horizon. We analyze the thermodynamics of the hairy black hole and find drastic changes in its thermodynamic structure due to the scalar field. For $f(\phi)=1$, there exists a critical value of the hairy parameter above which the charged hairy black hole exhibits the Hawking/Page phase transition, whereas no such phase transition occurs below this critical value. Similarly, for $f(\phi)=e^{-\phi}$ and $f(\phi)=e^{-\phi^2/2}$, the hairy solution exhibits a small/large black hole phase transition for above critical values of the hairy parameter. Interestingly, for these couplings, the thermodynamic phase diagram of three-dimensional hairy charged black holes resembles that of a higher-dimensional RN-AdS black hole, albeit with two second-order critical points.

##### 2.Quasinormal modes and grey-body factors of regular black holes with a scalar hair from the Effective Field Theory

**Authors:**R. A. Konoplya

**Abstract:** The Effective Field Theory (EFT) of perturbations on an arbitrary background geometry with a timelike scalar profile has been recently constructed in the context of scalar-tensor theories. Unlike General Relativity, the regular Hayward metric is realized as an exact background metric in the Effective Field Theory with timelike scalar profile without resorting to special matter field, such as nonlinear electrodynamics. The fundamental quasinormal mode for axial graviational perturbations of this black hole has been considered recently with the help of various methods. Here we make a further step in this direction and find that, unlike the fundamental mode, a few first overtones deviate from their Schwarzschild limit at a much higher rate. This outburst of overtones occurs because the overtones are extremely sensitive to the least change of the near-horizon geometry. The analytical formula for quasinormal modes is obtained in the eikonal regime. In addition, we calculated grey-body factors and showed that regular Hayward black hole with a scalar hair has smaller grey-body factor than the Schwarzschild one. Integration of the wave-like equation in time-domain shows that the power-law tails following the ring-down phase at late times are indistinguishable from the Schwarzschild ones.

##### 3.Limits of a non-local quantum spacetime

**Authors:**Dawood Kothawala

**Abstract:** A generic implication of incorporating gravitational effects in the analysis of quantum measurements is the existence of a zero-point length of spacetime. This requires an inherently non-local description of spacetime, beyond the usual one based on metric $g_{ab}(x)$ etc. The quantum spacetime should instead be reconstructed from non-local bi-tensors of the form $\mathscr{G}_{ab \ldots i'j' \ldots}(x,x')$. A deeper look then reveals a subtle interplay interplay between non-locality and the limit $G\hbar/c^3 \to 0$. In particular, the so called emergent gravity paradigm -- in which gravitational dynamics/action/spacetime are emergent and characterised by an *entropy functional* -- arises as the Cheshire grin of a fundamentally non-local quantum spacetime. This essay describes the flow of metric with respect to Planck length, and proposes a novel action for the same.

##### 4.Quantum Gravity Effect in Binary Black Hole Merger

**Authors:**Parthasarathi Majumdar

**Abstract:** We present a semi-rigorous justification of Bekenstein's Generalized Second Law of Thermodynamics applicable to a universe with black holes present, based on a generic quantum gravity formulation of a black hole spacetime, where the bulk Hamiltonian constraint plays a central role. Specializing to Loop Quantum Gravity, and considering the inspiral and post-ringdown stages of binary black hole merger into a remnant black hole, we show that the Generalized Second Law implies a lower bound on the non-perturbative LQG correction to the Bekenstein-Hawking area law for black hole entropy. This lower bound itself is expressed as a function of the Bekenstein-Hawking area formula for entropy. Using the analyses of LIGO-VIRGO-KAGRA data recently performed to verify the Hawking Area Theorem for binary black hole merger, this Loop Quantum Gravity-induced lower bound is shown to be entirely consistent with the data.

##### 5.Slowly rotating ultracompact Schwarzschild star in the gravastar limit

**Authors:**Philip Beltracchi, Camilo Posada

**Abstract:** We reconsider the problem of a slowly rotating homogeneous star, or Schwarzschild star, when its compactness goes beyond the Buchdahl bound and approaches the gravastar limit $R\to 2M$. We compute surface and integral properties of such configuration by integrating the Hartle-Thorne structure equations for slowly rotating relativistic masses, at second order in angular velocity. In the gravastar limit, we show that the metric of a slowly rotating Schwarzschild star agrees with the Kerr metric, thus, within this approximation, it is not possible to tell a gravastar from a Kerr black hole by any observations from the spacetime exterior to the horizon.

##### 6.Alleviation of anomalies from the non-oscillatory vacuum in loop quantum cosmology

**Authors:**Mercedes Martín-Benito, Rita B. Neves, Javier Olmedo

**Abstract:** In this work we investigate observational signatures of a primordial power spectrum with exponential infrared suppression, motivated by the choice of a non-oscillatory vacuum in a bouncing and inflationary geometry within Loop Quantum Cosmology (LQC). We leave the parameter that defines the scale at which suppression occurs free and perform a Bayesian analysis, comparing with CMB data. The data shows a preference for some of the suppression to be within the observable window. Guided by this analysis, we choose concrete illustrative values for this parameter. We show that the model affects only slightly the parity anomaly, but it is capable of alleviating the lensing and power suppression anomalies.

##### 7.Global and Local Stability for Ghosts Coupled to Positive Energy Degrees of Freedom

**Authors:**Cédric Deffayet, Aaron Held, Shinji Mukohyama, Alexander Vikman

**Abstract:** Negative kinetic energies correspond to ghost degrees of freedom, which are potentially of relevance for cosmology, quantum gravity, and high energy physics. We present a novel wide class of stable mechanical systems where a positive energy degree of freedom interacts with a ghost. These theories have Hamiltonians unbounded from above and from below, are integrable, and contain free functions. We show analytically that their classical motion is bounded for all initial data. Moreover, we derive conditions allowing for Lyapunov stable equilibrium points. A subclass of these stable systems has simple polynomial potentials with stable equilibrium points entirely due to interactions with the ghost. All these findings are fully supported by numerical computations which we also use to gather evidence for stability in various nonintegrable systems.

##### 8.Quantum Geometrodynamics Revived II. Hilbert Space of Positive Definite Metrics

**Authors:**Thorsten Lang, Susanne Schander

**Abstract:** This paper represents the second in a series of works aimed at reinvigorating the quantum geometrodynamics program. Our approach introduces a Hilbert space at each lattice site along with the corresponding representation of the conventional commutation relations, and which manifestly realizes the positive--definiteness of the spatial metric even in the quantum theory. To achieve this end, we resort to the Cholesky decomposition of the spatial metric into upper triangular matrices with positive diagonal entries. Moreover, our Hilbert space also carries a representation of the vielbein fields and naturally separates the physical and gauge degrees of freedom. Finally, we introduce a generalization of the Weyl quantization for our representation. We also emphasize that our proposed methodology is amenable to applications in other fields of physics, particularly in scenarios where the configuration space is restricted by complicated relationships among the degrees of freedom.

##### 1.Black hole shadow and Maximal Black room

**Authors:**Masaru Siino

**Abstract:** To comprehend the shadow of a black hole in a general spacetime, we have investigated the concept of the maximal black room (MBR). The boundary of the MBR is a non-spacelike hypersurface that contains at least one null geodesic tangent to its boundary, which we refer to as the rays' surface. Our aim is to explore the geometry of this surface. From our current study, we have observed that the boundary of the MBR is globally unstable. Leveraging this instability, we can determine the boundary based on the physical choice of the initial spacelike hypersurface and the orthogonal condition at that point. Upon examining the existence of the MBR, we can observe that it encompasses any arbitrary black hole. Additionally, we can investigate the possibility of using the MBR to differentiate a black hole from an exotic star with a photon sphere. In spherically symmetric spacetime, subject to energy conditions, the rays' surface encloses a black hole, a naked singularity, or exotic matter that has an inner universe.

##### 2.Emergence of the Gambier equation in cosmology

**Authors:**D. Batic, P. Guha, A. Ghose Choudhury

**Abstract:** We show how the Gambier equation arises in connection to Friedmann-Lema$\mbox{\^{i}}$tre-Robertson-Walker (FLRW) cosmology and a Dark Matter equation of state. Moreover, we provide a correspondence between the Friedmann equations and the Gambier equations that possess the Painlev$\acute{\mbox{e}}$ property in $2+1$ dimensions. We also consider special cases of the Gambier G27 equation such as the generalized Pinney equation. For an extended FLRW model with dynamic scalar field as matter model, the Einstein equations correspond to the Milne-Pinney equation which in turn can be mapped to the parametric Gambier equation of second order.

##### 3.Conserved charges of the Kerr black hole revisited

**Authors:**Okan Günel, Özgür Sarıoğlu

**Abstract:** We revisit the Kerr black hole as cast in the Boyer-Lindquist, Kerr-Schild and Weyl canonical coordinates, and calculate its total mass/energy and total angular momentum by using linearized gravity along with its background Killing isometries. We argue that the integration of the relevant gravitational flux does not depend on the geometry of the closed and simply connected spatial boundary provided it is also piecewise smooth.

##### 4.Universality in Binary Black Hole Dynamics: An Integrability Conjecture

**Authors:**José Luis Jaramillo, Badri Krishnan, Carlos F. Sopuerta

**Abstract:** The waveform of a binary black hole coalescence appears to be both simple and universal. In this essay we argue that the dynamics should admit a separation into 'fast and slow' degrees of freedom, such that the latter are described by an integrable system of equations, accounting for the simplicity and universality of the waveform. Given that Painlev\'e transcendents are a smoking gun of integrable structures, we propose the Painlev\'e-II transcendent as the key structural element threading a hierarchy of asymptotic models aiming at capturing different (effective) layers in the dynamics. Ward's conjecture relating integrable and (anti)self-dual solutions can provide the avenue to encode background binary black hole data in (non-local) twistor structures.

##### 5.Thermal analysis of photon-like particles in rainbow gravity

**Authors:**A. A. Araújo Filho, J. Furtado, H. Hassanabadi, J. A. A. S. Reis

**Abstract:** This work is devoted to study the thermodynamic behavior of photon--like particles within the \textit{rainbow} gravity formalism. To to do this, we chose two particular ansatzs to accomplish our calculations. First, we consider a dispersion relation which avoids UV divergences, getting a positive effective cosmological constant. We provide \textit{numerical} analysis for the thermodynamic functions of the system and bounds are estimated. Furthermore, a phase transition is also expected for this model. Second, we consider a dispersion relation employed in the context of \textit{Gamma Ray Bursts}. Remarkably, for this latter case, the thermodynamic properties are calculated in an \textit{analytical} manner and they turn out to depend on the harmonic series $H_{n}$, gamma $\Gamma(z)$, polygamma $\psi_{n}(z)$ and zeta Riemann functions $\zeta(z)$.

##### 6.Frenemies with Physicality: Manufacturing Manifold Metrics

**Authors:**Sebastian Schuster
Charles University of Prague

**Abstract:** Physicality has the bad habit of sneaking up on unsuspecting physicists. Unfortunately, it comes in multitudinous incarnations, which will not always make sense in a given situation. Breaching a warp drive metric with physical arguments is all good, but often what counts as physicality here is but a mere mask for something else. In times of analogue space-times and quantum effects, a more open mind is needed. Not only to avoid using a concept of physicality out of its natural habitat, but also to find useful toy models for our enlarged phenomenology of physics with metrics. This journey is bound to be as vexing, confusing, and subtle as it (hopefully) will be illuminating, entertaining, and thought-provoking.

##### 7.Complex conformal transformations and zero-rest-mass fields

**Authors:**Bernardo Araneda

**Abstract:** We give a simple prescription for relating different solutions to the zero-rest-mass field equations in conformally flat space-time via complex conformal transformations and changes in reality conditions. We give several examples including linearized black holes. In particular, we show that the linearized Plebanski-Demianski and Schwarzschild fields are related by a complex translation and a complex special conformal transformation. Similar results hold for the linearized Kerr and C-metric fields, and for a peculiar toroidal singularity.

##### 8.Bardeen Compact Stars in Modified \textbf{$f(R)$} Gravity with Conformal Motion

**Authors:**M. Farasat Shamir, Aisha Rashid

**Abstract:** The main emphasis of this paper is to find the viable solutions of Einstein Maxwell fields equations of compact star in context of modified $f(R)$ theory of gravity. Two different models of modified $f(R)$ gravity are considered. In particular, we choose isotropic matter distribution and Bardeen's model for compact star to find the boundary conditions as an exterior space-time geometry. We use the conformal Killing geometry to compute the metric potentials. We discuss the behavior of energy density and pressure distribution for both models. Moreover, we analyze different physical properties such as behavior of energy density and pressure, equilibrium conditions, equation of state parameters, causality conditions and adiabatic index. It is noticed that both $f(R)$ gravity models are suitable and provides viable results with Bardeen geometry.

##### 1.Relation between circular photon orbits and the stability of wormholes with the thin shell of a barotropic fluid

**Authors:**Naoki Tsukamoto, Takafumi Kokubu

**Abstract:** We cut a general, static, spherically symmetric spacetime which satisfying generalized Birkhoff's theorem and paste its copy to make a wormhole with a thin shell of any barotropic fluid in general relativity and we investigate the stability of the thin shell on a throat against linearized spherically symmetric perturbations. We show that the stability of the thin-shell wormhole satisfying a transparency condition which prohibits its momentum flux passing through the throat is characterized by circular photon orbits called (anti-)photon sphere in the original spacetime.

##### 2.The "neighborhood theorem" for the general relativistic characteristic Cauchy problem in higher dimension

**Authors:**Piotr T. Chrusciel, Roger Tagne Wafo, Finnian Gray

**Abstract:** We show that the maximal globally hyperbolic solution of the initial-value problem for the higher-dimensional vacuum Einstein equations on two transversally intersecting characteristic hypersurfaces contains a future neighborhood of the hypersurfaces.

##### 3.Remarks on stationary vacuum black holes

**Authors:**Piotr T. Chruściel

**Abstract:** We finish the proof of the no-hair theorem for stationary, analytic, connected, suitably regular, four dimensional vacuum black holes. We show how to define the surface gravity and the angular velocity of horizons without assuming analyticity. We point out that, under the usual regularity conditions, vacuum near-horizon geometries are Kerrian without assuming analyticity.

##### 4.Gödel's undecidability theorems and the search for a theory of everything

**Authors:**Claus Kiefer

**Abstract:** I investigate the question whether G\"odel's undecidability theorems play a crucial role in the search for a unified theory of physics. I conclude that unless the structure of space-time is fundamentally discrete we can never decide whether a given theory is the final one or not. This is relevant for both canonical quantum gravity and string theory.

##### 5.Black hole shadow and acceleration bounds for spherically symmetric spacetimes

**Authors:**Kajol Paithankar, Sanved Kolekar

**Abstract:** We explore an interesting connection between black hole shadow parameters and the acceleration bounds for radial linear uniformly accelerated (LUA) trajectories in static spherically symmetric black hole spacetime geometries. For an incoming radial LUA trajectory to escape back to infinity, there exists a bound on its magnitude of acceleration and the distance of closest approach from the event horizon of the black hole. We calculate these bounds and the shadow parameters, namely the photon sphere radius and the shadow radius, explicitly for specific black hole solutions in $d$-dimensional Einstein's theory of gravity, in pure Lovelock theory of gravity and in the $\mathcal{F}(R)$ theory of gravity. We find that for a particular boundary data, the photon sphere radius $r_{ph}$ is equal to the bound on radius of closest approach $r_b$ of the incoming radial LUA trajectory while the shadow radius $r_{sh}$ is equal to the inverse magnitude of the acceleration bound $|a|_b$ for the LUA trajectory to turn back to infinity. Using the effective potential technique, we further show that the same relations are valid in any theory of gravity for static spherically symmetric black hole geometries of the Schwarzschild type.

##### 6.A rotating modified JNW spacetime as a Kerr black hole mimicker

**Authors:**Kunal Pal, Kuntal Pal, Rajibul Shaikh, Tapobrata Sarkar

**Abstract:** The Event Horizon Telescope has recently observed the images and shadows of the compact objects M87$^*$ and Sgr A$^*$ at the centres of the galaxies Messier 87 and Milky Way. This has opened up a new window in observational astronomy to probe and test gravity and fundamental physics in the strong-field regime. In this paper, we consider a rotating version of a modified Janis-Newman-Winicour metric, study its shadow, and constrain the metric parameters using the observed shadows of M87$^*$ and Sgr A$^*$. Depending on parameter values, the spacetime metric represents either a naked singularity or a wormhole. We find that the naked singularity case is not consistent with observations, as it casts a shadow which is much smaller than the observed ones. On the other hand, the shadow formed by the wormhole branch, depending on the parameter values, is consistent with the observations. We put constraints on the wormhole throat radius by comparing the shadow with the observed ones of M87$^*$ and Sgr A$^*$.

##### 7.Wormholes and energy conditions in $f(R,T)$ gravity

**Authors:**Ayan Banerjee, Takol Tangphati, Anirudh Pradhan

**Abstract:** We explore the existence of wormholes in the context of $f(R,T)$ gravity. The $f(R,T)$ theory is a curvature-matter coupled modified gravity that depends on an arbitrary function of the Ricci scalar $R$ and the trace of the stress-energy tensor $T$. In this work, we adopt two different choices for the matter Lagrangian density ($\mathcal{L}_m= \mathcal{P}$ and $\mathcal{L}_m= p_r$) and investigate the impact of each one on wormhole structure. By adequately specifying the redshift function and the shape function, we found a variety of exact wormhole solutions in the theory. Our finding indicates that, for both classes of wormholes the energy density is always positive throughout the spacetime, while the radial pressure is negative. This means exotic matter is necessary for the existence of wormholes in $f(R,T)$ gravity.

##### 8.Probing the Origin of Primordial Black Holes through Novel Gravitational Wave Spectrum

**Authors:**Indra Kumar Banerjee, Ujjal Kumar Dey

**Abstract:** In this article we investigate the cumulative stochastic gravitational wave spectra as a tool to gain insight on the creation mechanism of primordial black holes. We consider gravitational waves from the production mechanism of primordial black holes and from the gravitational interactions of those primordial black holes among themselves and other astrophysical black holes. We specifically focus on asynchronous bubble nucleation during a first order phase transition as the creation mechanism. We have used two benchmark phase transitions through which the primordial black holes and the primary gravitational wave spectra have been generated. We have considered binary systems and close hyperbolic interactions of primordial black holes with other primordial and astrophysical black holes as the source of the secondary part of the spectra. We have shown that this unique cumulative spectra have features which directly and indirectly depend on the specifics of the production mechanism.

##### 9.Towards a bound on the Higgs mass in causal set quantum gravity

**Authors:**Gustavo P. de Brito, Astrid Eichhorn, Ludivine Fausten

**Abstract:** In the Standard Model of particle physics, the mass of the Higgs particle can be linked to the scale at which the Standard Model breaks down due to a Landau pole/triviality problem: for a Higgs mass somewhat higher than the measured value, the Standard Model breaks down before the Planck scale. We take a first step towards investigating this relation in the context of causal set quantum gravity. We use a scalar-field propagator that carries the imprints of spacetime discreteness in a modified ultraviolet behavior that depends on a nonlocality scale. We investigate whether the modification can shift the scale of the Landau pole in a scalar field theory with quartic interaction. We discover that the modifications speed up the onset of the Landau pole considerably, so that the scale of new physics occurs roughly at the nonlocality scale. Our results call into question, whether a separation between the nonlocality scale and the discreteness scale, which is postulated within causal set quantum gravity, and which has been argued to give rise to phenomenological consequences, is in fact achievable. Methodologically, our paper is the first to apply continuum functional Renormalization Group techniques in the context of a causal-set inspired setting.

##### 10.Dynamic Dark Energy from the Local Limit of Nonlocal Gravity

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

**Abstract:** Nonlocal gravity (NLG), a classical extension of Einstein's theory of gravitation, has been studied mainly in linearized form. In particular, nonlinearities have thus far prevented the treatment of cosmological models in NLG. In this essay, we discuss the local limit of NLG and apply this limit to the expanding homogenous and isotropic universe. The theory only allows spatially flat cosmological models; furthermore, de Sitter spacetime is forbidden. The components of the model will have different dynamics with respect to cosmic time as compared to the standard $\Lambda$CDM model; specifically, instead of the cosmological constant, the modified flat model of cosmology involves a dynamic dark energy component in order to account for the accelerated phase of the expansion of the universe.

##### 1.What are neutron stars made of? Gravitational waves may reveal the answer

**Authors:**Neil Lu, Susan M. Scott, Karl Wette

**Abstract:** Neutron stars are one of the most mysterious wonders in the Universe. Their extreme densities hint at new and exotic physics at work within. Gravitational waves could be the key to unlocking their secrets. In particular, a first detection of gravitational waves from rapidly-spinning, deformed neutron stars could yield new insights into the physics of matter at extreme densities and under strong gravity. Once a first detection is made, a critical challenge will be to robustly extract physically interesting information from the detected signals. In this essay, we describe initial research towards answering this challenge, and thereby unleashing the full power of gravitational waves as an engine for the discovery of new physics.

##### 2.Geodesically complete cyclic cosmologies and entropy

**Authors:**Petar Pavlović, Marko Sossich

**Abstract:** We demonstrate that there exists a class of cyclic cosmological models, such that these models can in principle solve the problem of the entropy growth, and are at the same time geodesically complete. We thus show that some recently stated conclusions, according to which cyclic cosmologies solving the problem of entropy growth can not be geodesically complete due to the Borde-Guth-Vilenkin (BGV) theorem, are not justified. We show that such types of geodesically complete models capable of solving the entropy growth problem fall in two main groups: the ones where the total average Hubble parameter is lesser or equal to zero, thus satisfying BGV theorem, and the ones for which BGV theorem is not applicable. We also add a short conceptual discussion on entropy and cyclic cosmology.

##### 3.Quantum gravity in the triangular gauge

**Authors:**Thomas Thiemann

**Abstract:** Vielbeins are necessary when coupling General Relativity (GR) to fermionic matter. This enhances the gauge group of GR to include local Lorentz transformations. In view of a reduced phase space formulation of quantum gravity, in this work we completely gauge fix that Lorentz gauge symmetry by using a so-called triangular gauge. Having solved the Gauss constraints already classically opens access to new Hilbert space representations which are free of the complications that otherwise arise due to a non Abelian gauge symmetry. In that sense, a connection formulation as being pursued in Loop Quantum Gravity is no longer the only practicable option and other less dimension dependent representations e.g. based on triads and even metrics suggest themselves. These formulations make it easier to identify states representing non-degenerate quantum geometries and thus to investigate the hypersurface deformation algebra which implicitly assumes non-degeneracy.

##### 4.Charged strange star model in Tolman-Kuchowicz spacetime in the background of 5D Einstein-Maxwell-Gauss-Bonnet gravity

**Authors:**Pramit Rej, Abdelghani Errehymy, Mohammed Daoud

**Abstract:** In this article, we provide a new model of static charged anisotropic fluid sphere made of a charged perfect fluid in the context of 5D Einstein-Maxwell-Gauss-Bonnet (EMGB) gravity theory. To generate exact solutions of the EMGB field equations, we utilize the well-behaved Tolman-Kuchowicz (TK) {\it ansatz} together with a linear equation of state (EoS) of the form $p_r=\beta \rho-\gamma$, (where $\beta$ and $\gamma$ are constants). Here the exterior space-time is described by the EGB Schwarzschild metric. The Gauss-Bonnet Lagrangian term $\mathcal{L}_{GB}$ is coupled with the Einstein-Hilbert action through the coupling constant $\alpha$. When $\alpha \to 0$, we obtain the general relativity (GR) results. Here we present the solution for the compact star candidate EXO 1785-248 with mass$=(1.3 \pm 0.2)M_{\odot}$; Radius $= 10_{-1}^{+1}$ km. respectively. We analyze the effect of this coupling constant $\alpha$ on the principal characteristics of our model, such as energy density, pressure components, anisotropy factor, sound speed etc. We compare these results with corresponding GR results. Moreover, we studied the hydrostatic equilibrium of the stellar system by using a modified Tolman-Oppenheimer-Volkoff (TOV) equation and the dynamical stability through the critical value of the radial adiabatic index.The mass-radius relationship is also established to determine the compactness factor and surface redshift of our model. In this way, the stellar model obtained here is found to satisfy the elementary physical requirements necessary for a physically viable stellar object.

##### 5.Post-Newtonian parameters of general scalar-tensor theories with and without an arbitrary scalar potential

**Authors:**Xing Zhang

**Abstract:** We study the parameterized post-Newtonian (PPN) metric of general scalar-tensor gravity with two arbitrary coupling functions in the two cases in which the scalar field has or does not have potential. We calculate all ten PPN parameters for a perfect fluid source in the case of a vanishing scalar potential and two PPN parameters $\gamma$ and $\beta$ for a point-like source in the case of a non-vanishing scalar potential, respectively. These PPN parameters are theory-dependent constants in the first case and distance-dependent in the second case. For a strong coupling scalar field with or without mass, or at the large distances limit, the PPN parameters $\gamma$ and $\beta$ tend to one. Our calculations can reduce to the previous results in simpler cases, including massless/massive Brans-Dicke theory.

##### 6.Traversable wormholes with double layer thin shells in quadratic gravity

**Authors:**Joao Luís Rosa, Rui André, José P. S. Lemos

**Abstract:** In quadratic gravity, the junction conditions are six and permit the appearance of double layer thin shells. Double layers arise typically in theories with dipoles, i.e., two opposite charges, such as electromagnetic theories, and appear exceptionally in gravitational theories, which are theories with a single charge. We explore this property of the existence of double layers in quadratic gravity to find and study traversable wormholes in which the two domains of the wormhole interior region, where the throat is located, are matched to two vacuum domains of the exterior region via the use of two double layer thin shells. The quadratic gravity we use is essentially given by a $R+\alpha R^2$ Lagrangian, where $R$ is the Ricci scalar of the spacetime and $\alpha$ is a coupling constant, plus a matter Lagrangian. The null energy condition, or NEC for short, is tested for the whole wormhole spacetime. The analysis shows that the NEC is satisfied for the stress-energy tensor of the matter in the whole wormhole interior region, notably at the throat, and is satisfied for some of the stress-energy tensor components of the matter at the double layer thin shell, but is not satisfied for some other components, namely, the double layer stress-energy distribution component, at the thin shell. This seems to mean that the NEC is basically impossible, or at least very hard, to be satisfied when double layer thin shells are present. Single layer thin shells are also admitted within the theory, and we present thin shell traversable wormholes, i.e., wormholes without interior, with a single layer thin shell at the throat for which the corresponding stress-energy tensor satisfies the NEC, that are asymmetric, i.e., with two different vacuum domains of the exterior region joined at the wormhole throat.

##### 7.Black hole entropy contributions from Euclidean cores

**Authors:**Jens Boos

**Abstract:** The entropy of a Schwarzschild black hole, as computed via the semiclassical Euclidean path integral in a stationary phase approximation, is determined not by the on-shell value of the action (which vanishes), but by the Gibbons--Hawking--York boundary term evaluated on a suitable hypersurface, which can be chosen arbitrarily far away from the horizon. For this reason, the black hole singularity seemingly has no influence on the Bekenstein--Hawking area law. In this Essay we estimate how a regular black hole core, deep inside a Euclidean black hole of mass $M$ and generated via a UV regulator length scale $\ell > 0$, affects the black hole entropy. The contributions are suppressed by factors of $\ell/(2GM)$; demanding exact agreement with the area law as well as a self-consistent first law of black hole thermodynamics at all orders, however, demands that these contributions vanish identically via uniformly bounded curvature. This links the limiting curvature hypothesis to black hole thermodynamics.

##### 8.Gravitational signatures of a non--commutative stable black hole

**Authors:**N. Heidari, H. Hassanabadi, A. A. Araújo Filho, J. Kuríuz, S. Zare, P. J. Porfírio

**Abstract:** This work investigates several key aspects of a non--commutative theory with mass deformation. We calculate thermodynamic properties of the system and compare our results with recent literature. We examine the \textit{quasinormal} modes of massless scalar perturbations using two approaches: the WKB approximation and the P\"oschl--Teller fitting method. Our results indicate that stronger non--commutative parameters lead to slower damping oscillations of gravitational waves and higher partial absorption cross sections. Furthermore, we study the geodesics of massless and massive particles, highlighting that the non--commutative parameter $\Theta$ significantly impacts the paths of light and event horizons. Also, we calculate the shadows, which show that larger values of $\Theta$ correspond to larger shadow radii. Finally, we explore the deflection angle and time delay in this context.

##### 9.On primordial gravitational waves in Teleparallel Gravity

**Authors:**Geovanny A. Rave-Franco, Celia Escamilla-Rivera

**Abstract:** Teleparallel Gravity is a gauge theory where gravity is a manifestation of the torsion of space-time and its success relies on being a possible solution to some problems of General Relativity. In this essay we introduce the construction of the theory by defining its geometrical setup, and how we can build it as a gauge theory of translations locally invariant under the Lorentz group. In this context, we will study the production of primordial gravitational waves and the observational implications when extended models are taken into account, particularly, we will notice how the tensor spectral index changes and produces a direct impact on the power spectrum from vacuum fluctuations and any source of tensor anisotropic stress in comparison to General Relativity.

##### 10.Spatially homogeneous teleparallel spacetimes with four-dimensional groups of motions

**Authors:**Manuel Hohmann

**Abstract:** We study metric teleparallel geometries, which can either be defined through a Lorentzian metric and flat, metric-compatible affine connection, or a tetrad and a flat spin connection, which are invariant under the transitive action of a four-dimensional Lie group on their spatial equal-time hypersurfaces. There are three such group actions, and their corresponding spatial hypersurfaces belong to the Bianchi types II, III and IX, respectively. For each of these three symmetry groups, we determine the most general teleparallel geometry, and find that it is parametrized by six functions of time, one of which can be eliminated by the choice of the time coordinate. We further show that these geometries are unique up to global Lorentz transformations, coordinate transformations and changes of the choice of the parameter functions.

##### 1.Riemann surface, Winding number and Black hole thermodynamics

**Authors:**Zhen-Ming Xu, Yu-Shan Wang, Bin Wu, Wen-Li Yang

**Abstract:** Phase transition is a very enlightening topic in black hole physics, which can largely demonstrate a certain quantum property of gravity. In this study, we use complex analysis to study the phase transition of the black hole thermodynamics system. By decomposing the obtained winding number, we can predict some characteristics of the phase transition of the system. There are three basic elements: (1) when the winding number is one, there is no phase transition, and the corresponding complex structure is the Riemann surface with one foliation; (2) the winding number is two, which corresponds to the second-order phase transition and has a Riemann surface with double foliations; (3) when the winding number is three, it means that the first order phase transition will occur, accompanied by the second order phase transition, which has a Riemann surface with three foliations. Especially, a black hole thermodynamics system with a triple point has a structure of the Riemann surface with five foliations.

##### 2.Effective no-hair relations for spinning Boson Stars

**Authors:**Christoph Adam, Jorge Castelo, Alberto García Martín-Caro, Miguel Huidobro, Andrzej Wereszczynski

**Abstract:** Boson Stars are, at present, hypothetical compact stellar objects whose existence, however, could resolve several enigmas of current astrophysics. If they exist, either as independent astrophysical entities or as a matter admixture of more standard compact stars, then their imprints can probably be observed in the not-too-distant future from the gravitational signal of coalescing binaries in current and future GW detectors. Here we show that the multipole moments of rotating boson stars obey certain universal relations, valid for a broad set of models and various states in terms of the \textit{harmonic indices}. These universal relations are equivalent to a kind of no-hair theorem for this exotic matter, allowing to map these universal (i.e. model independent) multipoles to an equally universal gravitational field around the stellar object. Further, the multipole moments can be related to observable astrophysical quantities.

##### 3.Testing Gravity in the Laboratory

**Authors:**Quentin G. Bailey

**Abstract:** In this chapter, we discuss recent work on precision Earth laboratory tests of different aspects of gravity. In particular the discussion is focused on those tests that can be used to probe hypothesis for physics beyond Newtonian gravity and General Relativity. The latter includes tests of foundations like local Lorentz invariance, Weak-Equivalence Principle tests, short-range gravity tests, gravimeter-type tests, and other frontier possibilities like the free-fall of anti-matter and searches for non-Riemann gravity effects. The focus is on key results in theory, phenomenology, and experiment in the last few decades. We describe the motivations for continued interest in precision tests of gravity in the laboratory, including the possibility to search for physics beyond General Relativity. Test frameworks for describing deviations from General Relativity are emphasized, including ones based on effective field theory, allowing for generic violations of Lorentz symmetry, CPT symmetry, and diffeomorphism symmetry.

##### 1.Instability of scalarized compact objects in Einstein-scalar-Gauss-Bonnet theories

**Authors:**Masato Minamitsuji, Shinji Mukohyama

**Abstract:** We investigate the linear stability of scalarized black holes (BHs) and neutron stars (NSs) in the Einstein-scalar-Gauss-Bonnet (GB) theories against the odd- and even-parity perturbations including the higher multipole modes. We show that the angular propagation speeds in the even-parity perturbations in the $\ell \to \infty$ limit, with $\ell$ being the angular multipole moments, become imaginary and hence scalarized BH solutions suffer from the gradient instability. We show that such an instability appears irrespective of the structure of the higher-order terms in the GB coupling function and is caused purely due to the existence of the leading quadratic term and the boundary condition that the value of the scalar field vanishes at the spatial infinity.~This indicates that the gradient instability appears at the point in the mass-charge diagram where the scalarized branches bifurcate from the Schwarzschild branch. We also show that scalarized BH solutions realized in a nonlinear scalarization model also suffer from the gradient instability in the even-parity perturbations. Our result also suggests the gradient instability of the exterior solutions of the static and spherically-symmetric scalarized NS solutions induced by the same GB coupling functions.

##### 2.Cosmological dynamical systems analysis of scalar-tensor $f(R,T)$ gravity

**Authors:**Tiago B. Gonçalves, João Luís Rosa, Francisco S. N. Lobo

**Abstract:** In this work, we use the dynamical system approach to explore the cosmological background evolution of the recently proposed scalar-tensor representation of $f(R,T)$ gravity, where $R$ is the Ricci scalar and $T$ is the trace of the stress-energy tensor. A motivation for this work resides in finding cosmological models that undergo a transition from a decelerating epoch into an accelerated one without the need of an exotic fluid with negative pressure. More specifically, we study two classes of models of the geometry-matter coupling in this theory, namely, in the first case, we consider an addition of an $R$-term with a $T$-term, and in the second case, we analyse a stronger coupling that allows for the appearance of crossed $RT$ terms. Our results indicate that both models feature a significant region of their phase space corresponding to cosmological models with accelerated expansion, and several trajectories in the phase space can evolve into this region from a decelerated phase. In particular, we verify that the first of these geometry-matter couplings successfully models the cosmological evolution towards a de-Sitter behaviour, without the necessity of recurring to a cosmological constant. A general feature of these theories with geometry-matter couplings is the non-conservation of the stress-energy tensor. However, in the first approach in our analysis, we have imposed $\nabla^{\mu} T_{\mu\nu}=0$, which is helpful as an additional constraint to solve the system of dynamical equations. Then, in a second approach, we briefly explore the general case $\nabla^{\mu} T_{\mu\nu} \neq 0$, finding that the second class of models with stronger matter-geometry coupling also becomes adequate to model a transition into a de-Sitter-like solution.

##### 3.Closer look at cosmological consequences of interacting group field theory

**Authors:**Maxime De Sousa, Aurélien Barrau, Killian Martineau

**Abstract:** Group field theory has shown to be a promising framework to derive cosmological predictions from full quantum gravity. In this brief note, we revisit the background dynamics when interaction terms are taken into account and conclude that, although the bounce is clearly robust, providing a geometrical explanation for inflation seems to be very difficult. We consider possible improvements and modifications of the original scenario and derive several limits on the parameters of the model.

##### 4.On the algebraic classification of the gravitational field in Weyl-Cartan space-times

**Authors:**Sebastian Bahamonde, Jorge Gigante Valcarcel

**Abstract:** We present a complete algebraic classification for the curvature tensor in Weyl-Cartan geometry, by applying methods of eigenvalues and principal null directions on its irreducible decomposition under the group of global Lorentz transformations, thus providing a full invariant characterisation of all the possible algebraic types of the torsion and nonmetricity field strength tensors in Weyl-Cartan space-times. As an application, we show that in the framework of Metric-Affine Gravity the field strength tensors of a dynamical torsion field cannot be doubly aligned with the principal null directions of the Riemannian Weyl tensor in scalar-flat stationary and axisymmetric space-times.

##### 5.Inflationary Attractors Predictions for Static Neutron Stars in the Mass-Gap Region

**Authors:**S. D. Odintsov, V. K. Oikonomou

**Abstract:** In this work we study static neutron stars in the context of several inflationary models which are popular in cosmology. These inflationary models are non-minimally coupled scalar theories which yield a viable inflationary phenomenology in both Jordan and Einstein frames. By considering the constraints from inflationary theories, which basically determine the values of the potential strength, usually considered as a free parameter in astrophysical neutron star works, we construct and solve the Tolman-Oppenheimer-Volkoff equations using a solid python-3 LSODA integrator. For our study we consider several popular inflationary models, such as the universal attractors, the $R^p$ attractors (three distinct model values), the induced inflation, the quadratic inflation, the Higgs inflation and the $a$-attractors (two distinct model values) and for the following popular equations of state the WFF1, the SLy, the APR, the MS1, the AP3, the AP4, the ENG, the MPA1 and the MS1b. We construct the $M-R$ diagram and we confront the resulting theory with theoretical and observational constraints. As we demonstrate, remarkably, all the neutron stars produced by all the inflationary models we considered are compatible with all the constraints for the MPA1 equation of state. It is notable that for this particular equation of state, the maximum masses of the neutron stars are in the mass-gap region with $M>2.5M_{\odot}$, but lower than the 3 solar masses causal limit. We also make the observation that as the NICER constraints are pushed towards larger radii, as for example in the case of the black widow pulsar PSR J0952-0607, it seems that equations of state that produce neutron stars with maximum masses in the mass gap region, with $M>2.5M_{\odot}$, but lower than the 3 solar masses causal limit, are favored and are compatible with the modified NICER constraints.

##### 6.Topological classification and black hole thermodynamics

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

**Abstract:** One of the new methods that can be used to study the thermodynamics critical points of a system based on a topological approach is the study of topological charges using Duan's $\phi$-mapping method. In this article, we will attempt to use this method to study three different black holes, each with different coefficients in their metric function, in order to determine the class of critical points these black holes have in terms of phase transition. Through this analysis, we found that the Euler-Heisenberg black hole has two different topological classes, and the parameter $"a"$ added to the metric function by QED plays an important role in this classification. While a black hole with a non-linear electrodynamic field, despite having an electromagnetic parameter, which is added to its metric function, has only one topological class, and its $"\alpha"$ parameter has no effect on the number of critical points and topological class. Finally, the Young Mills black hole in massive gravity will have a different number of critical points depending on the coefficient $"c_i"$, which is related to massive gravity and leads to different topological classes. However, this black hole exhibits the same phase structure in all cases.

##### 7.Performance of the low-latency GstLAL inspiral search towards LIGO, Virgo, and KAGRA's fourth observing run

**Authors:**Becca Ewing, Rachael Huxford, Divya Singh, Leo Tsukada, Chad Hanna, Yun-Jing Huang, Prathamesh Joshi, Alvin K. Y. Li, Ryan Magee, Cody Messick, Alex Pace, Anarya Ray, Surabhi Sachdev, Shio Sakon, Ron Tapia, Shomik Adhicary, Pratyusava Baral, Amanda Baylor, Kipp Cannon, Sarah Caudill, Sushant Sharma Chaudhary, Michael W. Coughlin, Bryce Cousins, Jolien D. E. Creighton, Reed Essick, Heather Fong, Richard N. George, Patrick Godwin, Reiko Harada, James Kennington, Soichiro Kuwahara, Duncan Meacher, Soichiro Morisaki, Debnandini Mukherjee, Wanting Niu, Cort Posnansky, Andrew Toivonen, Takuya Tsutsui, Koh Ueno, Aaron Viets, Leslie Wade, Madeline Wade, Gaurav Waratkar

**Abstract:** GstLAL is a stream-based matched-filtering search pipeline aiming at the prompt discovery of gravitational waves from compact binary coalescences such as the mergers of black holes and neutron stars. Over the past three observation runs by the LIGO, Virgo, and KAGRA (LVK) collaboration, the GstLAL search pipeline has participated in several tens of gravitational wave discoveries. The fourth observing run (O4) is set to begin in May 2023 and is expected to see the discovery of many new and interesting gravitational wave signals which will inform our understanding of astrophysics and cosmology. We describe the current configuration of the GstLAL low-latency search and show its readiness for the upcoming observation run by presenting its performance on a mock data challenge. The mock data challenge includes 40 days of LIGO Hanford, LIGO Livingston, and Virgo strain data along with an injection campaign in order to fully characterize the performance of the search. We find an improved performance in terms of detection rate and significance estimation as compared to that observed in the O3 online analysis. The improvements are attributed to several incremental advances in the likelihood ratio ranking statistic computation and the method of background estimation.

##### 1.Exploring the nature of black hole and gravity with an imminent merging binary of supermassive black holes

**Authors:**Xingyu Zhong, Wenbiao Han, Ziren Luo, Yueliang Wu

**Abstract:** A supermassive binary black-hole candidate SDSS J1430+2303 reported recently motivates us to investigate an imminent binary of supermassive black holes as potential gravitational wave source, the radiated gravitational waves at the end of the merger are shown to be in the band of space-borne detectors. We provide a general analysis on the required detecting sensitivity needed for probing such type gravitational wave sources and make a full discussion by considering two typically designed configurations of space-borne antennas. If a source is so close, it is possible to be detected with Taiji pathfinder-plus which is proposed to be an extension for the planned Taiji pathfinder by just adding an additional satellite to the initial two satellites. The gravitational wave detection on such kind of source enables us to explore the properties of supermassive black holes and the nature of gravity.

##### 2.Boson star with parity-odd symmetry in wormhole spacetime

**Authors:**Yuan Yue, Peng-Bo Ding, Yong-Qiang Wang

**Abstract:** In this paper, we revisit the model of bosonic matter in the form of a free complex scalar field with a nontrivial wormhole spacetime topology supported by a free phantom field. We obtain a new type of boson star with wormhole solutions, in which the complex scalar field possess full parity-odd symmetry with respect to the two asymptotically flat spacetime regions. When the size of the throat is small, The behavior of boson stars with wormhole approaches that of boson stars. When the size of the throat is intermediate, the typical spiraling dependence of the mass and the particle number on the frequency of the boson stars is replaced by a loop structure. However, as the size becomes relatively large, the loop structure will also disappear. In particular, The complex scalar field could form two boson stars with opposite phase differences with respect to the two spacetime regions in the limit of vanishing throat size. We analyze the properties of this new type of boson stars with wormhole and further show that the wormhole spacetime geometry.

##### 3.On networks of space-based gravitational-wave detectors

**Authors:**Rong-Gen Cai, Zong-Kuan Guo, Bin Hu, Chang Liu, Youjun Lu, Wei-Tou Ni, Wen-Hong Ruan, Naoki Seto, Gang Wang, Yue-Liang Wu

**Abstract:** The space-based laser interferometers, LISA, Taiji and TianQin, are targeting to observe milliHz gravitational waves (GWs) in the 2030s. The joint observations from multiple space-based detectors yield significant advantages. In this work, we recap the studies and investigations for the joint space-based GW detector networks to highlight: 1) the high precision of sky localization for the massive binary black hole (BBH) coalescences and the GW sirens in the cosmological implication, 2) the effectiveness to test the parity violation in the stochastic GW background observations, 3) the efficiency of subtracting galactic foreground, 4) the improvement in stellar-mass BBH observations. We inspect alternative networks by trading off massive BBH observations and stochastic GW background observation.

##### 4.Transformation of mass-angular momentum aspect under BMS transformations

**Authors:**Po-Ning Chen, Mu-Tao Wang, Ye-Kai Wang, Shing-Tung Yau

**Abstract:** In this article, we present the definitive transformation formulae of the mass aspect and angular momentum aspect under BMS transformations. Two different approaches that lead to the same formulae are taken. In the first approach, the formulae are derived by reading off the aspect functions from the curvature tensor. While in the second and more traditional approach, we read them off from the metric coefficients. As an application of the angular momentum aspect transformation formula, we directly verify a relation concerning the Dray-Streubel angular momentum. It also enables us to reinterpret our calculations in terms of differential forms on null infinity, and leads to an exact expression of the Drey-Streubel angular momentum of a general section. The formulae we obtained played crucial roles in our recent work on supertranslation invariant charges, and resolved some inconsistencies in the literature.

##### 5.Exploring departures from Schwarzschild black hole geometry in $f(R)$ gravity

**Authors:**Vittorio De Falco, Francesco Bajardi, Rocco D'Agostino, Micol Benetti, Salvatore Capozziello

**Abstract:** Different astrophysical methods can be combined to detect possible deviations from General Relativity. In this work, we consider a class of $f(R)$ gravity models selected by the existence of Noether symmetries. In this framework, it is possible to determine a set of static and spherically symmetric black hole solutions, encompassing small departures from the Schwarzschild geometry. In particular, when gravity is the only dominating interaction, we exploit the ray-tracing technique to reconstruct the image of a black hole, the epicyclic frequencies, and the black hole shadow profile. Moreover, when matter dynamics is also affected by an electromagnetic radiation force, we take into account the general relativistic Poynting-Robertson effect. In light of the obtained results, the proposed strategy results to be robust and efficient: on the one hand, it allows to investigate gravity from strong to weak field regimes; on the other hand, it is capable of detecting small departures from General Relativity, depending on the current observational sensitivity.

##### 6.Regular rotating black hole: to Kerr or not to Kerr?

**Authors:**Alexander Kamenshchik, Polina Petriakova

**Abstract:** We examine the Newman-Janis algorithm's application to an exact regular static solution sustained by a minimally coupled scalar field with a non-standard kinetic term. Although coordinate complexification leads to a regular Kerr-like black hole, we are facing discrepancies in Einstein's equations in a fairly small domain, for which the regularizing parameter is responsible. Outside this most intriguing region, the geometry is nothing but the standard Kerr spacetime.

##### 7.Geometric structures of Morris-Thorne wormhole metric in $f(R,L_m)$ gravity and energy conditions

**Authors:**V. Venkatesha, N. S. Kavya, P. K. Sahoo

**Abstract:** The aim of this manuscript is to study the traversable wormhole (WH) geometries in the curvature matter coupling gravity. We investigate static spherically symmetric Morris-Thorne WHs within the context of $f(R,L_m)$ gravity. To accomplish this, we examine the WH model in four different cases (i) linear $f(R,L_m)$ model, $f(R,L_m)=\alpha R+\beta L_m$ with anisotropic matter distribution having the relation $p_r=m p_t$ (ii) linear $f(R,L_m)$ model having anisotropic matter distribution along with the equation of state parameter, $p_r=\omega \rho$, (iii) non-linear model $f(R,L_m)=\dfrac{1}{2}R+L_m^\eta$ with specific form of energy density and (iv) non-linear $f(R,L_m)$ model, $f(R,L_m)=\dfrac{1}{2}R+(1+\xi R)L_m$ with isotropic matter distribution and having the linear relation between pressure and energy density, $p=\omega \rho$. Additionally, in the latter case, we consider a specific power-law shape function $b(r)=r_0 \left(\dfrac{r_0}{r}\right)^n$. Furthermore, we analyze the energy conditions for each WH model to verify their physical viability. As a novel outcome, we can see the validation of the null energy condition for the $f(R,L_m)$ model that suggests ruling out the necessity of exotic matter for the traversability of the WH. At last, an embedding diagram for each model is illustrated that describes the WH geometry.

##### 8.Heavier tail likelihoods for robustness against data outliers: Applications to the analysis of gravitational wave data

**Authors:**Argyro Sasli, Nikolaos Karnesis, Nikolaos Stergioulas

**Abstract:** In recent years, the field of Gravitational Wave Astronomy has flourished. With the advent of more sophisticated ground-based detectors and space-based observatories, it is anticipated that Gravitational Wave events will be detected at a much higher rate in the near future. One of the future data analysis challenges, is performing robust statistical inference in the presence of detector noise transients or non-stationarities, as well as in the presence of stochastic Gravitational Wave signals of possible astrophysical origin. The incomplete knowledge of instrumental noise can introduce bias in parameter estimation of detected sources. Here, we propose a heavier-tailed likelihood filter based on the Generalized Hyperbolic distribution. With the Hyperbolic likelihood we obtain a robust data analysis framework against data outliers, noise non-stationarities, and possible inaccurate modeling of the noise power spectral density. We apply this methodology to examples drawn from gravitational wave astronomy, and in particular using synthetic data sets from the planned LISA mission, demonstrating its effectiveness in improving parameter estimation accuracy. Our findings suggest that the use of heavier-tailed likelihoods can significantly improve the robustness of statistical inference in Gravitational Wave Astronomy.

##### 9.Memory matters : Gravitational wave memory of compact binary coalescence in the presence of matter effects

**Authors:**Dixeena Lopez, Shubhanshu Tiwari, Michael Ebersold

**Abstract:** Binary neutron stars (BNS) and neutron star-black hole (NSBH) binaries are one of the most promising gravitational wave (GW) sources to probe matter effects. Upcoming observing runs of LIGO-Virgo-KAGRA detectors and future third generation detectors like Einstein Telescope and Cosmic Explorer will allow the extraction of detailed information on these matter effects from the GW signature of BNS and NSBH systems. One subtle effect which may be helpful to extract more information from the detection of compact binary systems is the non-linear memory. In this work, we investigate the observational consequences of gravitational wave non-linear memory in the presence of matter effects. We start by quantifying the impact of non-linear memory on distinguishing BNS mergers from binary black holes (BBH) or NSBH mergers. We find that for the third generation detectors, the addition of non-linear memory to the GW signal model expands the parameter space where BNS signals become distinguishable from the BBH and NSBH signals. Using numerical relativity simulations, we also study the non-linear memory generated from the post-merger phase of BNS systems. We find that it does not show a strong dependence on the equation of state of the NS. However, the non-linear memory from the BNS post-merger phase is much lower than the one from BBH systems of the same masses. Furthermore, we compute the detection prospects of non-linear memory from the post-merger phase of NS systems by accumulating signal strength from a population of BNS mergers for the current and future detectors. Finally, we discuss the impact of possible linear memory from the dynamical ejecta of BNS and NSBH systems and its signal strength relative to the non-linear memory. We find that linear memory almost always has a much weaker effect than non-linear memory.

##### 10.The gravitational two-body potential generated by binary systems

**Authors:**Renato Spigler

**Abstract:** We evaluate the {\em three-dimensional}, {\em non-axis-symmetric}, {\em time-dependent} Newton potential generated by a pair of mutually orbiting objects such as pairs of ordinary or neutron stars and, in some approximations, black holes, spinning around each other. The `vertical component' of the gravitational force (that is, that orthogonal to the plane of their orbit) is also evaluated, along with the other components of the field. The pseudo-Newtonian Paczy\'{n}ski-Wiita form of the potential is also computed. The effect of the asymmetry due to the more common case of different masses is stressed.

##### 11.Electrically charged regular black holes in nonlinear electrodynamics: light rings, shadows and gravitational lensing

**Authors:**Marco A. A. de Paula, Haroldo C. D. Lima Junior, Pedro V. P. Cunha, Luís C. B. Crispino

**Abstract:** Within nonlinear electrodynamics (NED), photons follow null geodesics of an effective geometry, which is different from the geometry of the spacetime itself. Over the last years, several works were dedicated to investigate the motion of photons in the effective geometry of NED-based magnetically charged regular black hole (RBH) solutions. However, there are few works considering electrically charged RBHs. We study the light rings, shadows, and gravitational lensing of the electrically charged RBH solution proposed by Irina Dymnikova (ID), which is a static and spherically symmetric spacetime with a NED source. We show that the shadow associated to the effective geometry can be almost 10% bigger that the one associated to the standard geometry. We also find that the ID solution may mimic the shadow properties of the Reissner-Nordstr\"om (RN) BH, for low-to-extreme values of the electric charge. Besides that, by using the backwards ray-tracing technique, we obtain that ID and RN BH solutions can have a very similar gravitational lensing, for some values of the correspondent electric charges. We also show that the motion of photons in the effective geometry can be interpreted as a non-geodesic curve submitted to a 4-force term, from the perspective of an observer in the standard geometry.

##### 12.Incompleteness Theorems for Observables in General Relativity

**Authors:**Aristotelis Panagiotopoulos, George Sparling, Marios Christodoulou

**Abstract:** The quest for complete observables in general relativity has been a longstanding open problem. We employ methods from descriptive set theory to show that no complete observable is Borel definable. In fact, we show that it is consistent with the Zermelo-Fraenkel and Dependent Choice axioms that no complete observable exists whatsoever. In a nutshell, this implies that the Problem of Observables is to`analysis' what the Delian Problem was to `straightedge and compass'. Our results remain true even after restricting the space of solutions to vacuum solutions. In other words, the issue can be traced to the presence of local degrees of freedom in general relativity.

##### 13.Ideal Gas Thermodynamics with an Invariant Energy Scale

**Authors:**Sudipta Das

**Abstract:** A viable approach towards Quantum Gravity is the Doubly Special Relativity (DSR) framework in which an observer-independent finite energy upper bound (or a finite smallest length scale) appears quite naturally. In this work, we have studied the thermodynamic properties of an ideal gas in a specific DSR framework, known as the Magueijo-Smolin (MS) Model. We use the fact that DSR can be considered as nonlinear representation of Lorentz Group. Subsequently, various thermodynamic parameters of ideal gas have been derived in this modified framework to compare the corresponding deviations from the usual scenario due to the presence of the invariant energy (length) scale.

##### 14.Chaos and Einstein-Rosen waves

**Authors:**Sebastian J. Szybka, Syed U. Naqvi

**Abstract:** We demonstrate the existence of chaotic geodesics for the Einstein-Rosen standing gravitational waves. The complex dynamics of massive test particles are governed by a chaotic heteroclinic network. We present the fractal associated with the system under investigation. Gravitational standing waves produce intricate patterns through test particles in a vague analogy to mechanical vibrations generating Chladni figures and complicated shapes of Faraday waves.

##### 1.Rotating black strings in ModMax theory

**Authors:**Hamid R. Bakhtiarizadeh, Hanif Golchin

**Abstract:** In this paper, we investigate the asymptotically Anti de Sitter solutions of rotating black strings coupled to ModMax non-linear electrodynamics. By studying the near-horizon behavior of solutions, we find the mass, surface gravity and accordingly the Hawking temperature. We also compute the entropy, the total mass, the angular momentum, the charge, and the electrostatic potential of solutions and show that the first law of thermodynamics for rotating black strings is hold, in the presence of a ModMax nonlinear source. We also check thermal stability of solutions and observe that they have negative specific heat, which makes them thermodynamically unstable.

##### 2.Non-exotic static spherically symmetric thin-shell wormhole solution in $f(Q,T)$ gravity

**Authors:**Moreshwar Tayde, Sayantan Ghosh, P. K. Sahoo

**Abstract:** In this study, we have conducted an analysis of traversable wormhole solutions within the framework of linear $f(Q, T) = \alpha Q + \beta T$ gravity, ensuring that all the energy conditions hold for the entire spacetime. The solutions presented in this study were derived through a comprehensive analytical examination of the parameter space associated with the wormhole model. This involved considering the exponents governing the redshift and shape functions, as well as the radius of the wormhole throat ($r_0$), the redshift function value at the throat ($\phi_0$), and the model parameters ($\alpha$ and $\beta$). Also, we have established bounds on these free parameters that guarantee the satisfaction of the energy conditions throughout spacetime and have also provided two solutions. Further, we have used the Israel junction condition to see the stability of a thin-shell around the wormhole. We have also calculated the NEC criteria and potential for such a thin-shell and how it varies with the chosen shape function.

##### 3.Static spherically symmetric solutions in New General Relativity

**Authors:**Alexey Golovnev, A. N. Semenova, V. P. Vandeev

**Abstract:** We give a pedagogical introduction to static spherically symmetric solutions in models of New GR, both explaining the basics and showing how all such vacuum solutions can be obtained in elementary functions. In doing so, we coherently introduce the full landscape of these modified teleparallel spacetimes, and find a few special cases. The equations of motion are turned into a very nice and compact form by using the Levi-Civita divergence of the torsion-conjugate; and generalised Bianchi identities are briefly discussed. Another important point we make is that a convenient choice of the radial variable might be instrumental for success of similar studies in other modified gravity models.

##### 4.Teleparallel bigravity

**Authors:**Daniel Blixt, Manuel Hohmann, Tomi Koivisto, Luca Marzola

**Abstract:** We write down the teleparallel equivalent to Hassan-Rosen bigravity, which is written using a torsionful but curvature-free connection. The theories only differ by a boundary term. The equivalence was proven, both by using perturbation theory and Hamiltonian analysis. It is further shown how one can construct novel bigravity theories within the teleparallel framework. Some of those are analyzed through perturbation theory, and it is found that all of the considered novel bigravity theories suffer from pathologies. In particular, it is found that a construction with two copies of new general relativity leads to ghostly degrees of freedom which are not present in the single tetrad teleparallel corresponding theory. We demonstrate how the teleparallel framework allows to easily create theories with derivative interaction. However, it is shown through perturbation theory that the simplest model is not viable. Furthermore, we demonstrate some steps in the Hamiltonian analysis of teleparallel bigravity with two copies of new general relativity and some toy models. The results rule out some of the novel teleparallel bigravity theories, but also demonstrate techniques in perturbation theory and Hamiltonian analysis which could be further used for more profound theories in the future.

##### 5.Tilt-to-length coupling in LISA Pathfinder: analytical modelling

**Authors:**Marie-Sophie Hartig, Gudrun Wanner

**Abstract:** Tilt-to-length coupling was the limiting noise source in LISA Pathfinder between 20 and 200 mHz before subtraction in post-processing. To prevent the adding of sensing noise to the data by the subtraction process, the success of this strategy depended on a previous direct noise reduction by test mass alignment. The exact dependency of the level of tilt-to-length coupling on the set-points of LISA Pathfinder's test masses was not understood until the end of the mission. Here, we present, for the first time, an analytical tilt-to-length coupling model that describes the coupling noise changes due to the realignments. We report on the different mechanisms, namely the lever arm and piston effect as well as the coupling due to transmissive components, and how they contribute to the full coupling. Further, we show that a pure geometric model would not have been sufficient to describe the coupling in LISA Pathfinder. Therefore, we model also the non-geometric tilt-to-length noise contributions. For the resulting coupling coefficients of the full model, we compute the expected error bars based on the known individual error sources. Also, we validated the analytical model against numerical simulations. A detailed study and thorough understanding of this noise are the basis for a successful analysis of the LISA Pathfinder data with respect to tilt-to-length coupling.

##### 1.Quasinormal modes of the Bardeen black hole with a cloud of strings

**Authors:**Yunlong Liu, Xiangdong Zhang

**Abstract:** We investigate the quasinormal mode and greybody factor of Bardeen black holes with a string clouds by WKB approximation and verify them by Prony algorithm. We found that the imaginary part of the quasinormal modes spectra is always negative and the perturbation does not increase with the time, indicating that the system is stable under scalar field perturbation. Moreover, the string parameter $a$ has a dramatically impact on the frequency and decay rate of the waveforms. In addition, the greybody factor becomes larger when $a$ and $\lambda$ increase while $q$ and $l$ decreases. The parameter $\lambda$ and $l$ have a big effect on the tails. Especially, when $l=0$, a de Sitter phase appears at the tail.

##### 2.Prospects for an isotropic gravitational wave background detection with Earth-based interferometric detectors and the threat of correlated noise

**Authors:**Kamiel Janssens

**Abstract:** In this overview we discuss the prospects for a first detection of an isotropic gravitational wave background with earth-based interferometric detectors. Furthermore, we focus on how correlated noise sources could endanger such a detection with current generation of detectors. Finally, we project how correlated noise could significantly impede the potential of the future detector, the Einstein Telescope, in its search for an isotropic gravitational wave background. The triangular configuration of three (almost) co-located detectors, makes the Einstein Telescope especially prone to correlated noise sources.

##### 3.Impact of electric charges on chaos in magnetized $Reissner-Nordström$ spacetimes

**Authors:**Daqi Yang, Wenfang Liu, Xin Wu

**Abstract:** We consider the motion of test particles around a $Reissner-Nordstr\"{o}m$ black hole immersed into a strong external magnetic field modifying the spacetime structure. When the particles are neutral, their dynamics are nonintegrable because the magnetic field acts as a gravitational effect, which destroys the existence of a fourth motion constant in the $Reissner-Nordstr\"{o}m$ spacetime. A time-transformed explicit symplectic integrator is used to show that the motion of neutral particles can be chaotic under some circumstances. When test particles have electric charges, their motions are subject to an electromagnetic field surrounding the black hole as well as the gravitational forces from the black hole and the magnetic field. It is found that increasing both the magnetic field and the particle energy or decreasing the particle angular momentum can strengthen the degree of chaos regardless of whether the particles are neutral or charged. The effect of varying the black hole positive charge on the dynamical transition from order to chaos is associated with the electric charges of particles. The dynamical transition of neutral particles has no sensitive dependence on a change of the black hole charge. An increase of the black hole charge weakens the chaoticity of positive charged particles, whereas enhances the chaoticity of negative charged particles. With the magnitude of particle charge increasing, chaos always gets stronger.

##### 4.Gravitational Wave from Domain Walls in $f(G)$ Theory

**Authors:**S. P. Hatkar, S. P. Saraogi, S. D. Katore

**Abstract:** In this paper, we have studied Bianchi type I space-time in the presence of domain walls in the context of $f(G)$ theory of gravitation. Field equations are solved by using the special form of deceleration parameter. It is also assumed that expansion is proportional to the shear scalar of the model. Some physical parameters are discussed in detail.

##### 5.Is the Universe anisotropic right now? Comparing the real Universe with the Kasner's space-time

**Authors:**S L Parnovsky

**Abstract:** We investigate possible astronomical manifestations of space-time anisotropy. The homogeneous vacuum Kasner solution was chosen as a reference anisotropic cosmological model because there are no effects caused by inhomogeneity in this simple model with a constant degree of anisotropy. This anisotropy cannot become weak. The study of its geodesic structure made it possible to clarify the properties of this space-time. It showed that the degree of manifestation of anisotropy varies significantly depending on the travel time of the light from the observed object. For nearby objects, for which it does not exceed half the age of the universe, the manifestations of anisotropy are very small. Distant objects show more pronounced manifestations, for example, in the distribution of objects over the sky and over photometric distances. These effects for each of the individual objects decrease with time, but in general, the manifestations of anisotropy in the Kasner space-time remain constant due to the fact that new sources emerging from beyond the cosmological horizon.We analyse observable signatures of the Kasner-type anisotropy and compare it to observations. These effects were not found in astronomical observations, including the study of the CMB. We can assume that the Universe has always been isotropic or almost isotropic since the recombination era. This does not exclude the possibility of its significant anisotropy at the moment of the Big Bang followed by rapid isotropization during the inflationary epoch.

##### 6.Looking for static interior solutions of Buchdahl star with $p_r=0, p_t=kρ$ in general relativity and pure Lovelock theories

**Authors:**Shauvik Biswas, Chiranjeeb Singha

**Abstract:** We find static fluid solutions of Einstein and pure Lovelock equations with $p_r=0$, $p_t=k\rho$, which could be possible models for the interior of a Buchdahl-like star. Buchdahl star is a limiting stellar configuration without a horizon whose formation does not need any exotic matter.

##### 7.Little Rip, Pseudo Rip and bounce cosmology from generalized equation of state in the Universe with spatial curvature

**Authors:**A. V. Timoshkin, A. V. Yurov

**Abstract:** We consider the Little Rip (LR), Pseudo Rip (PR) and bounce cosmological models in the Friedmann-Robertson-Walker (FRW) metric with nonzero spatial curvature. We describe the evolution of the universe using a generalized equation of state in the presence of a viscous fluid. The conditions of the occurrence of the LR, PR and bounce were obtained from the point of view of the parameters of the generalized equation of state for the cosmic dark fluid, taking into account the spatial curvature. The analytical expressions for the spatial curvature were obtained. Asymptotic cases of the early and late universe are considered. A method of Darboux transformation was proposed in the case of models of an accelerating universe with viscosity.

##### 8.Critical behavior of AdS black holes surrounded by dark fluid with Chaplygin-like equation of state

**Authors:**Xiang-Qian Li, Hao-Peng Yan, Li-Li Xing, Shi-Wei Zhou

**Abstract:** Supposing the existence of Dark Fluid with a Chaplygin-like equation of state $p=-B/\rho$ (CDF) as a cosmic background, we obtain a static spherically-symmetric black hole (BH) solution to the Einstein gravitational equations. We study the $P-V$ critical behavior of AdS BH surrounded by the CDF in the extended phase space where the cosmological constant appears as pressure, and our results show the existence of the Van der Waals like small/large BH phase transition. Also, it is found that such a BH displays a first-order low/high-$\Phi$ BH phase transition and admits the same criticality with van der Waals liquid/gas system in the non-extended phase space, where the normalization factor $q$ is considered as a thermodynamic variable, while the cosmological constant being fixed. In both $P-V$ and the newly proposed $q-\Phi$ phase spaces, we calculate the BH equations of state and then numerically study the corresponding critical quantities. Moreover, the critical exponents are derived and the results show the universal class of the scaling behavior of thermodynamic quantities near criticality. Finally, we study the shadow thermodynamics of AdS BHs surrounded by the CDF. We find that, there exists a positive correlation between the shadow radius and the event horizon radius in our case. By analyzing the temperature and heat capacity curves under the shadow context, we discover that the shadow radius can replace the event horizon radius to demonstrate the BH phase transition process, and the changes of the shadow radius can serve as order parameters for the small/large BH phase transition, indicating that the shadow radius could give us a glimpse into the BH phase structure from the observational point of view.

##### 1.Noether gauge symmetry approach applying for the non-minimally coupled gravity to the Maxwell field

**Authors:**S. Mahmoudi, S. Hajkhalili, S. H. Hendi

**Abstract:** Taking the Noether gauge symmetry approach into account, we find spherically symmetric static black hole solutions of the non-minimal gauge-gravity Lagrangian of the $\mathcal{R}^\beta F^2$ model. At first, we consider a system of differential equations for the general non-minimal couplings of $Y(\mathcal{R})F^2$ type, and then, we regard a particular $\mathcal{R}^\beta F^2$ non-minimal model to find the exact black hole solution and analyze its symmetries. As the next step, we calculate the thermodynamical quantities of the black hole and study its interesting behavior. Besides, we address thermal stability and examine the possibility of the van der Waals-like phase transition.

##### 2.The c-completion of Lorentzian metric spaces

**Authors:**Saúl Burgos, José Luis Flores, Jónatan Herrera

**Abstract:** Inspired by some Lorentzian versions of the notion of metric and length space introduced by Kunzinger and S\"amman, and more recently, by M\"uller, and Minguzzi and S\"uhr, we construct the c-completion of these models by previously discussing the notion of Lorentzian metric space. We not only prove that this construction is applicable to very general Lorentzian metric spaces, including spacetimes of low regularity, but also endow the c-completion with a structure of Lorentzian metric space by itself. We also prove that the c-completion constitutes a well-suited extension of the original space, which is sensible to certain causal properties of that space.

##### 3.Dynamic aether as a trigger for spontaneous spinorization in early Universe

**Authors:**Alexander B. Balakin, Anna O. Efremova

**Abstract:** In the framework of the Einstein-Dirac-aether theory we consider a phenomenological model of the spontaneous growth of the fermion number, which is triggered by the dynamic aether. The trigger version of spinorization of the early Universe is associated with two mechanisms: the first one is the aetheric regulation of behavior of the spinor field; the second mechanism can be related to a self-similarity of internal interactions in the spinor field. The dynamic aether is designed to switch on and switch off the self-similar mechanism of the spinor field evolution; from the mathematical point of view, the key of such a guidance is made of the scalar of expansion of the aether flow, proportional to the Hubble function in the isotropic cosmological model. Two phenomenological parameters of the presented model are shown to be considered as factors predetermining the total number of fermions born in the early Universe.

##### 4.Israel-Wilson-Perjes Metrics in a Theory with a Dilaton Field

**Authors:**Metin Gurses, Tahsin Cagri Sisman, Bayram Tekin

**Abstract:** We are interested in the charged dust solutions of the Einstein field equations in stationary and axially symmetric spacetimes; and inquire if the naked singularities of the Israel-Wilson-Perjes (IWP) metrics can be removed. The answer is negative in four dimensions. We examine whether this negative result can be avoided by adding scalar or dilaton fields. We show that IWP metrics also arise as solutions of the Einstein-Maxwell system with a stealth dilaton field. We determine the IWP metrics completely in terms of one complex function satisfying the Laplace equation. With the inclusion of the stealth dilaton field, it is now possible to add a perfect fluid source. In this case the field equations reduce to a complex cubic equation. Hence this procedure provides interior solutions to each IWP metric; and it is possible to cover all naked singularities inside a compact surface where there is matter distribution.

##### 5.Stability and instability results for equilibria of a (relativistic) self-gravitating collisionless gas -- A review

**Authors:**Gerhard Rein

**Abstract:** We review stability and instability results for self-gravitating matter distributions, where the matter model is a collisionless gas as described by the Vlasov equation. The focus is on the general relativistic situation, i.e., on steady states of the Einstein-Vlasov system and their stability properties. In order to put things into perspective we include the Vlasov-Poisson system and the relativistic Vlasov-Poisson system into the discussion.

##### 1.Testing the FLRW metric with the Hubble and transversal BAO measurements

**Authors:**Min Wang, Xiangyun Fu, Bing Xu, Ying Yang, Zhaoxia Chen

**Abstract:** The cosmological principle is one of the fundamental assumptions of the standard model of Cosmology (SCM), and it allow us to describe cosmic distances and clocks by using the Friedmann-Lema$\rm{\hat{{\i}}}$tre-Roberton-Walker (FLRW) metric. Thus, it is essential to test the FLRW metric with cosmological observations to verify the validity of the SCM. In this work, we perform tests of the FLRW metric by comparing the observational comoving angles between the Hubble $H(z)$ and angular Baryon Acoustic Oscillation (BAO) measurements. The Gaussian process is employed to reconstruct the Hubble $H(z)$ measurements and the angular diameter distance (ADD) from the transversal BAO data. A non-parametric method is adopted to probe the possible deviations from the FLRW metric at any redshift by comparing the comoving distances from the reconstructed Hubble $H(z)$ measurements with the ADD reconstructed from the transversal BAO data. Then, we propose two types of parameterizations for the deviations from the FLRW metric, and test the FLRW metric by using the priors of specific sound horizon scales. To avoid the bias caused by the prior of a specific sound horizon scale, we perform the consistency test with a flat prior of the sound horizon scale. We find that there a concordance between the FLRW metric and the observational data by using parametric and non-parametric methods, and the parameterizations can be employed to test the FLRW metric in a new way independent of the sound horizon scale.

##### 2.Weyl geometric effects on the propagation of light in gravitational fields

**Authors:**Marius A. Oancea, Tiberiu Harko

**Abstract:** We consider the effects of Weyl geometry on the propagation of electromagnetic waves and on the gravitational spin Hall effect of light. It is usually assumed that in vacuum the electromagnetic waves propagate along null geodesics, a result which follows from the geometrical optics approximation. However, this model is valid only in the limit of infinitely high frequencies. At large but finite frequencies, the ray dynamics is affected by the wave polarization. Therefore, the propagation of the electromagnetic waves can deviate from null geodesics, and this phenomenon is known as the gravitational spin Hall effect of light. On the other hand, Maxwell's equations have the remarkable property of conformal invariance. This property is a cornerstone of Weyl geometry and the corresponding gravitational theories. As a first step in our study, we obtain the polarization-dependent ray equations in Weyl geometry, describing the gravitational spin Hall effect of light in the presence of nonmetricity. As a specific example of the spin Hall effect of light in Weyl geometry, we consider the case of the simplest conformally invariant action, constructed from the square of the Weyl scalar, and the strength of the Weyl vector only. The action is linearized in the Weyl scalar by introducing an auxiliary scalar field. In static spherical symmetry, this theory admits an exact black hole solution, which generalizes the standard Schwarzschild solution through the presence of two new terms in the metric, having a linear and a quadratic dependence on the radial coordinate. We numerically study the polarization-dependent propagation of light rays in this exact Weyl geometric metric, and the effects of the presence of the Weyl vector on the magnitude of the spin Hall effect are estimated.

##### 3.Search for the $f(R,T)$ gravity functional form via gaussian processes

**Authors:**J. A. S. Fortunato, P. H. R. S. Moraes, J. G. de Lima Júnior, E. Brito

**Abstract:** The $f(R,T)$ gravity models, for which $R$ is the Ricci scalar and $T$ is the trace of the energy-momentum tensor, elevate the degrees of freedom of the renowned $f(R)$ theories, by making the Einstein field equations of the theory to also depend on $T$. While such a dependence can be motivated by quantum effects, the existence of imperfect or extra fluids, or even a cosmological ``constant'' which effectively depends on $T$, the formalism can truly surpass some deficiencies of $f(R)$ gravity. As the $f(R,T)$ function is arbitrary, several parametric models have been proposed {\it ad hoc} in the literature and posteriorly confronted with observational data. In the present article, we use gaussian process to construct an $f(R,T)=R+f(T)$ model. To apply the gaussian process we use a series of measurements of the Hubble parameter. We then analytically obtain the functional form of the function. By construction, this form, which is novel in the literature, is well-adjusted to cosmological data. In addition, by extrapolating our reconstruction to redshift $z=0$, we were able to constrain the Hubble constant value to $H_0=69.97\pm4.13$$\rm \ km \ s^{-1} \ Mpc^{-1}$ with $5\%$ precision. Lastly, we encourage the application of the functional form herewith obtained to other current problems of observational cosmology and astrophysics, such as the rotation curves of galaxies.

##### 4.On 1 + 3 covariant perturbations of the quasi-Newtonian space-time in modified Gauss-Bonnet gravity

**Authors:**Albert Munyeshyaka, Joseph Ntahompagaze, Tom Mutabazi, Manasse. R Mbonye

**Abstract:** The consideration of a 1 + 3 covariant approach to cold dark matter universe with no shear cosmological dust model with irrotational flows is developed in the context of f (G) gravity theory in the present study. This approach reveals the existence of integrability conditions which do not appear in non-covariant treatments. We constructed the integrability conditions in modified Gauss-Bonnet f (G) gravity basing on the constraints and propagation equations. These integrability conditions reveal the linearized silent nature of quasi-Newtonian models in f (G) gravity. Finally, the linear equations for the overdensity and velocity perturbations of the quasi-Newtonian space-time were constructed in the context of modified f (G) gravity. The application of harmonic decomposition and redshift transformation techniques to explore the behaviour of the overdensity and velocity perturbations using f (G) model were made. On the other hand we applied the quasi-static approximation to study the approximated solutions on small scales which helps to get both analytical and numerical results of the perturbation equations. The analysis of the energy overdensity and velocity perturbations for both short and long wavelength modes in a dust-Gauss-Bonnet fluids were done and we see that both energy overdensity and velocity perturbations decay with redshift for both modes. In the limits to {\Lambda}CDM , it means f (G) = G the considered f (G) model results coincide with {\Lambda}CDM .

##### 5.Effect of acceleration on information scrambling

**Authors:**Xi Ming

**Abstract:** The research subjects of information scrambling and the Unruh (anti-Unruh) effect are closely associated with black hole physics. We study the impact of acceleration on information scrambling under the Unruh (anti-Unruh) effect for two types of tripartite entangled states, namely the GHZ and W states. Our findings indicate that the anti-Unruh effect can result in stronger information scrambling, as measured by tripartite mutual information (TMI). Additionally, we show that the W state is more stable than the GHZ state under the influence of uniformly accelerated motion. Lastly, we extend our analysis to $N$-partite entangled states and product states.

##### 6.Gödel-type universes in energy-momentum-squared gravity

**Authors:**Á. J. C. Canuto, A. F. Santos

**Abstract:** In this paper, a modification of general relativity is considered. It consists of generalizing the Lagrangian of matter in a non-linear way, that is, replacing the curvature scalar $R$ by a function $f(R,T_{\mu\nu} T^{\mu\nu} )$, where $T_{\mu\nu}$ is the energy-momentum tensor. The main objective is to investigate the issue of causality in this gravitational model. To study the causality and/or its violation the G\"{o}del-type solutions are used. For such development, different matter contents are chosen. A critical radius, beyond which causality is violated, is calculated. It is shown that both causal and non-causal solutions are allowed.

##### 7.Observable Gravitational Waves from Hyperkination in Palatini Gravity and Beyond

**Authors:**Samuel Sánchez López, Konstantinos Dimopoulos, Alexandros Karam, Eemeli Tomberg

**Abstract:** We consider cosmology with an inflaton scalar field with an additional quartic kinetic term. Such a theory can be motivated by Palatini $R+R^2$ modified gravity. Assuming a runaway inflaton potential, we take the Universe to become dominated by the kinetic energy density of the scalar field after inflation. Initially, the leading kinetic term is quartic and we call the corresponding period hyperkination. Subsequently, the usual quadratic kinetic term takes over and we have regular kination, until reheating. We study, both analytically and numerically, the spectrum of primordial gravitational waves generated during inflation and re-entering the horizon during the subsequent eras. We demonstrate that the spectrum is flat for modes re-entering during radiation domination and hyperkination and linear in frequency for modes re-entering during kination: kinetic domination boosts the spectrum, but hyperkination truncates its peak. As a result, the effects of the kinetic period can be extended to observable frequencies without generating excessive gravitational waves, which could otherwise destabilise the process of Big Bang Nucleosynthesis. We show that there is ample parameter space for the primordial gravitational waves to be observable in the near future. If observed, the amplitude and `knee' of the spectrum will provide valuable insights into the background theory.

##### 8.Primordial black holes formation in a early matter dominated era from the pre-big bang scenario

**Authors:**Conzinu P., Marozzi G

**Abstract:** We discuss the production of primordial black holes in an early matter dominated era, which typically takes place in string inspired early universe cosmological models. In particular, we consider a pre-big bang scenario (extending previous results regarding formation in the radiation dominated era) where the enhancement of curvature perturbations is induced by a variation of the sound-speed parameter c_s during the string phase of high-curvature inflation. After imposing all relevant observational constraints, we find that the considered class of models is compatible with the production of a large amount of primordial black holes, in the mass range relevant to dark matter, only for a small range of the parameters space. On the other hand, we find that a huge production of light primordial black holes may occur both in such matter dominated era and in the radiation dominated one.

##### 9.Static traversable wormhole solutions in $f(R,L_m)$ gravity

**Authors:**N. S. Kavya, V. Venkatesha, G. Mustafa, P. K. Sahoo, S. V. Divya Rashmi

**Abstract:** In this study, we explore the new wormhole solutions in the framework of new modified $f(R,L_m)$ gravity. To obtain a characteristic wormhole solution, we use anisotropic matter distribution and a specific form of energy density. As second adopt the isotropic case with a linear EoS relation as a general technique for the system and discuss several physical attributes of the system under the wormhole geometry. Detailed analytical and graphical discussion about the matter contents via energy conditions is discussed. In both cases, the shape function of wormhole geometry satisfies the required conditions. Several interesting points have evolved from the entire investigation along with the features of the exotic matter within the wormhole geometry. Finally, we have concluding remarks.

##### 10.Ameliorating the Courant-Friedrichs-Lewy condition in spherical coordinates: A double FFT filter method for general relativistic MHD in dynamical spacetimes

**Authors:**Liwei Ji, Vassilios Mewes, Yosef Zlochower, Lorenzo Ennoggi, Federico G. Lopez Armengol, Manuela Campanelli, Federico Cipolletta, Zachariah B. Etienne

**Abstract:** Numerical simulations of merging compact objects and their remnants form the theoretical foundation for gravitational wave and multi-messenger astronomy. While Cartesian-coordinate-based adaptive mesh refinement is commonly used for simulations, spherical-like coordinates are more suitable for nearly spherical remnants and azimuthal flows due to lower numerical dissipation in the evolution of fluid angular momentum, as well as requiring fewer numbers of computational cells. However, the use of spherical coordinates to numerically solve hyperbolic partial differential equations can result in severe Courant-Friedrichs-Lewy (CFL) stability condition timestep limitations, which can make simulations prohibitively expensive. This paper addresses this issue for the numerical solution of coupled spacetime and general relativistic magnetohydrodynamics evolutions by introducing a double FFT filter and implementing it within the fully MPI-parallelized SphericalNR framework in the Einstein Toolkit. We demonstrate the effectiveness and robustness of the filtering algorithm by applying it to a number of challenging code tests, and show that it passes these tests effectively, demonstrating convergence while also increasing the timestep significantly compared to unfiltered simulations.

##### 11.GW_CLASS: Cosmological Gravitational Wave Background in the Cosmic Linear Anisotropy Solving System

**Authors:**Florian Schulze, Lorenzo Valbusa Dall'Armi, Julien Lesgourgues, Angelo Ricciardone, Nicola Bartolo, Daniele Bertacca, Christian Fidler, Sabino Matarrese

**Abstract:** The anisotropies of the Cosmological Gravitational Wave Background (CGWB) retain information about the primordial mechanisms that source the gravitational waves and about the geometry and the particle content of the universe at early times. In this work, we discuss in detail the computation of the angular power spectra of CGWB anisotropies and of their cross correlation with Cosmic Microwave Background (CMB) anisotropies, assuming different processes for the generation of these primordial signals. We present an efficient implementation of our results in a modified version of CLASS which will be publicly available. By combining our new code GW_CLASS with MontePython, we forecast the combined sensitivity of future gravitational wave interferometers and CMB experiments to the cosmological parameters that characterize the cosmological gravitational wave background.

##### 12.Post-Newtonian Generation of Gravitational Waves in a Theory of Gravity with Torsion

**Authors:**M. Schweizer, N. Straumann, A. Wipf

**Abstract:** We adapt the post-Newtonian gravitational-radiation methods developed within general relativity by Epstein and Wagoner to the gravitation theory with torsion, recently proposed by Hehl et al., and show that the two theories predict in this approximation the same gravitational radiation losses. Since they agree also on the first post-Newtonian level, they are at the present time - observationally - indistinguishable.

##### 13.Cosmic acceleration in entropic cosmology

**Authors:**Javier Chagoya, I. Díaz-Saldaña, J. C. López-Domínguez, M. Sabido

**Abstract:** In this paper we study the viability of an entropic cosmological model. The effects of entropic gravity are derived from a modified entropy-area relationship with a volumetric entropy term. This model describes a late time limit {cosmic acceleration}, whose origin is related to a volumetric term in the entropy. Moreover, we analyze the phenomenological implications of the entropic model using the Supernovae {\it Pantheon} compilation and the observational Hubble parameter data to find consistency with cosmological observations. Finally, we show the equivalence between the entropic model and a brane world cosmological model, by means of an effective geometrical construction.

##### 14.Quantum strong cosmic censorship and black hole evaporation

**Authors:**Benito A. Juárez-Aubry

**Abstract:** It is common folklore that semiclassical gravity suggests that, in the process of black hole formation and subsequent evaporation by Hawking radiation, an initially pure state can evolve into a mixed state. This is known as the \emph{information loss puzzle} (or {\it paradox}). Here, we argue that a quantum version of strong cosmic censorship, for which we give a conjectural statement and has strong supporting evidence, indicates that the semiclassical description of the evaporation process breaks down at the final evaporation stage. We argue further that, if taken at face value, semiclassical gravity predicts the development of a future singularity instead of a post-evaporation region where quantum (and classical) predictability breaks down and where information is lost. We thus argue that there are no reasons to expect a failure of unitarity or predictability for any quantum gravity theory that can `cure' spacetime singularities, as this is not even suggested by semiclassical arguments.

##### 15.Spontaneous pair production near magnetized Reissner-Nordstrom black holes

**Authors:**Haryanto M. Siahaan

**Abstract:** We investigate the pair production near a (near) extremal magnetized Reissner-Nordstrom black hole. The pair production is shown to exist in the extremal state, which can be interpreted as the Schwinger effect due to the strong field under consideration. To show a correspondence between the growth of the external magnetic field and the scalar absorption, some numerical examples are provided.

##### 1.Black Holes with Scalar Hair in Three Dimensions

**Authors:**Thanasis Karakasis, George Koutsoumbas, Eleftherios Papantonopoulos

**Abstract:** Three - dimensional static and spinning black hole solutions of the Einstein-Klein-Gordon system are obtained for a particular scalar field configuration. At large distances, and for small scalar field, the solutions reduce to the BTZ black hole. The scalar field dresses the black hole with secondary scalar hair, since the scalar charge is related to the conserved black hole mass and is not an independent charge. A self interacting potential is included, containing a mass term that is above the Breitenlohner-Freedman bound in three dimensions. Independence of the scalar potential from the conserved black hole charges, imposes fixed mass and angular momentum to scalar charge ratios. The thermodynamic properties as well as the energy conditions of the black hole are analysed.

##### 2.The Hawking Energy in a Perturbed Friedmann-Lemaître Universe

**Authors:**Dennis Stock, Enea Di Dio, Ruth Durrer

**Abstract:** Hawking's quasi-local energy definition quantifies the energy enclosed by a spacelike 2-sphere in terms of the amount of lightbending on the sphere caused by the energy distribution inside the sphere. This paper establishes for the first time a direct connection between the formal mathematical definition of a quasi-local energy and observations, in the context of cosmological perturbation theory. This is achieved by studying the Hawking Energy of spherical sections of the past lightcone of a cosmic observer in a perturbed Friedmann-Lema\^{i}tre spacetime. We express the Hawking Energy in terms of gauge-invariant perturbation variables and comment on the cosmic observables needed to in principle measure it. We then calculate its angular power spectrum and interpret its contributions.

##### 3.Novel high-frequency gravitational waves detection with split cavity

**Authors:**Chu-Tian Gao, Yu Gao, Yiming Liu, Sichun Sun

**Abstract:** Gravitational waves can generate electromagnetic effects inside a strong electric or magnetic field within the Standard Model and general relativity. Here we propose using a quarterly split cavity and LC-resonance circuit to detect a high-frequency gravitational wave from 0.1 MHz to GHz. We perform a full 3D simulation of the cavity's signal for sensitivity estimate. Our sensitivity depends on the coherence time scale of the high-frequency gravitational wave sources and the volume size of the split cavity. We discuss the resonant measurement schemes for narrow-band gravitational wave sources and also a non-resonance scheme for broadband signals. For a meter-sized split cavity under a 14 Tesla magnetic field, the LC resonance enhanced sensitivity to the gravitational wave strain is expected to reach $h\sim 10^{-20}$ around $10$ MHz.

##### 1.Limitations in Testing the Lense-Thirring Effect with LAGEOS and the Newly Launched Geodetic Satellite LARES 2

**Authors:**Lorenzo Iorio

**Abstract:** The new geodetic satellite LARES 2, cousin of LAGEOS and sharing with it almost the same orbital parameters apart from the inclination, displaced by 180 deg, was launched last year. Its proponents suggest using the sum of the nodes of LAGEOS and of LARES 2 to measure the sum of the Lense-Thirring node precessions independently of the systematic bias caused by the even zonal harmonics of the geopotential, claiming a final $\simeq 0.2$ percent total accuracy. In fact, the actual orbital configurations of the two satellites do not allow one to attain the sought for mutual cancellation of their classical node precessions due to the Earth's quadrupole mass moment, as their sum is still $\simeq 5000$ times larger than the added general relativistic rates. This has important consequences. One is that the current uncertainties in the eccentricities and the inclinations of both satellites do not presently allow the stated accuracy goal to be met, needing improvements of 3-4 orders of magnitude. Furthermore, the imperfect knowledge of the Earth's angular momentum $S$ impacts the uncancelled sum of the node precessions, from 150 to 4900 percent of the relativistic signal depending on the uncertainty assumed in $S$. It is finally remarked that the real breakthrough in reliably testing the gravitomagnetic field of the Earth would consist in modeling it and simultaneously estimating one or more dedicated parameter(s) along with other ones characterising the geopotential, as is customarily performed for any other dynamical feature.

##### 2.Shadows and Quasinormal modes of the Bardeen black hole in cloud of strings

**Authors:**Bijendra Kumar Vishvakarma, Dharm Veer Singh, Sanjay Siwach

**Abstract:** We investigate the black hole (BH) solution of the Einstein's gravity coupled with non-linear electrodynamics (NED) source in the background of a cloud of strings. We analyze the horizon structure, regularity, and energy conditions of the obtained BH solution. The optical features of the BH are explored. The photon radius and shadows of the BH are obtained as a function of black hole parameters. We observe that the size of the shadow image is bigger than its horizon radius and photon sphere. We also study the Quasinormal modes (QNM) using WKB formula for this black hole. The dependence of shadow radius and QN modes on black hole parameters reflects that they are mimicker to each other.

##### 3.Robustness of predicted CMB fluctuations in Cartan $F(R)$ gravity

**Authors:**Tomohiro Inagaki, Hiroki Sakamoto, Masahiko Taniguchi

**Abstract:** The cosmology of the $F(R)$ gravity rebuilding by the Cartan formalism is investigated. This is called Cartan $F(R)$ gravity. The well-known $F(R)$ gravity has been introduced to extend the standard cosmology, e.g. to explain the cosmological accelerated expansion as the inflation. Cartan $F(R)$ gravity is based on the Riemann-Cartan geometry. The curvature $R$ can separate to two parts, one is derived from the Levi-Civita connection and the other from the torsion. Assuming the matter-independent spin connection, we have successfully rewritten the action of Cartan $F(R)$ gravity into the Einstein-Hilbert action and a scalar field with canonical kinetic and potential terms without any conformal transformations. This feature simplifies building and analysis of new model of inflation. In this paper, we study two models, the power-law model and logarithmic model, and evaluate fluctuations in the cosmological microwave background (CMB) radiation. We found the robustness of CMB fluctuation by the analytical computation and confirm this feature by the numerical calculation.

##### 4.Generating spacetimes from colliding sources

**Authors:**M. Halilsoy, V. Memari

**Abstract:** Certain well-known spacetimes of general relativity (GR) are generated from the collision of suitable null-sources coupled with gravitational waves. This is a classical process underlying the full nonlinearity of GR that may be considered alternative to the quantum creativity at a large scale. Schwarzschild, de Sitter, anti de Sitter and the $\gamma $-metrics are given as examples.

##### 5.Test of the Second Postulate of Relativity from Gravitational Wave Observations

**Authors:**Rajes Ghosh, Sreejith Nair, Lalit Pathak, Sudipta Sarkar, Anand S. Sengupta

**Abstract:** The second postulate of special relativity states that the speed of light in vacuum is independent of the emitter's motion. Though this claim has been verified in various experiments and observations involving electromagnetic radiation with very high accuracy, such a test for gravitational radiation still needs to be explored. We analyzed data from the LIGO and Virgo detectors to test this postulate for gravitational radiation within the ambit of \textit{emission models}, where the speed of gravitational waves emitted by a source moving with a velocity $v$ relative to a stationary observer is given by ${c' = c + k\,v}$, where $k$ is a constant. We have estimated the upper bound on the 90\% credible interval over $k$ that parameterizes the deviation from the second postulate to be ${k \leq 8.3 \times {10}^{-18}}$ which is several orders of magnitude more stringent compared to previous bounds obtained from electromagnetic observations. The Bayes' factor supports the second postulate, with very strong evidence that the data is consistent with the null hypothesis $k = 0$. This confirms that the speed of gravity is independent of the motion of the emitter, upholding the principle of relativity for gravitational interactions.

##### 1.Gravitational Perturbation in Nonlocal Modified Tolman VII

**Authors:**Byon N. Jayawiguna, Piyabut Burikham

**Abstract:** Modified Tolman VII (MTVII), in the presence of an additional parameter, can increase the compactness of compact object. If the compactness is in the ultracompact regime, the quasinormal modes~(QNMs) of the trapped mode as well as the gravitational echoes can be more viable. Starting with the MTVII model, we introduce nonlocality into the matter sector and analyze the effective potential, the QNMs, and the gravitational echoes of the compact and ultracompact object in the nonlocal model. The nonlocal gravity version of MTVII~(NGMTVII) is parametrized by the nonlocal parameters~($\tilde{\beta} $), free parameter ($ \alpha $), and the compactness ($ \mathcal{C}$). We have found that NGMTVII can reach $ \mathcal{C}_{max}=0.414 $ with $ \tilde{\beta}_{max} = 3 $ and $ \alpha=0, $ which is significantly more compact than the MTVII model. We have also found that for relatively small value of $\tilde{\beta}$ and the compactness $ \mathcal{C} \lesssim 0.277$~(with $M=2.15$ solar masses, $R=11.5$ km at $\mathcal{C}=0.277$), the causality condition and the dominant energy condition~(DEC) are satisfied. For the perturbation, the quasinormal modes are calculated using Bohr-Sommerfeld (BS) fitting and it is found that the nonlocality produces more trapped modes than the original (MTVII) counterpart. At high compactness, gravitational echoes are simulated numerically.

##### 2.Detecting Fundamental Vector Fields with LISA

**Authors:**Shaun David Brocus Fell, Lavinia Heisenberg, Doğa Veske

**Abstract:** The advent of gravitational wave astronomy has seen a huge influx of new predictions for potential discoveries of beyond the Standard Model fields. The coupling of all fundamental fields to gravity, together with its dominance on large scales, makes gravitational physics a rich laboratory to study fundamental physics. This holds especially true for the search for the elusive dark photon, a promising dark matter candidate. The dark photon is predicted to generate instabilities in a rotating black hole spacetime, birthing a macroscopic Bose-Einstein condensate. These condensates can especially form around super massive black holes, modifying the dynamical inspiralling process. This then opens another window to leverage future space-borne gravitational wave antennas to join the hunt for the elusive dark matter particle. This study builds a preliminary model for the gravitational waveform emitted by such a dressed extreme mass-ratio inspiral. Comparing these waveforms to the vacuum scenario allows projections to the potential constrainability on the dark photon mass by space-borne gravitational wave antennas. The superradiant instability of a massive vector field on a Kerr background is calculated and the modification to the dynamics of an inspiralling solar mass-scale compact object is determined with approximations on the backreaction effect of the cloud on the compact object. The end result is the projection that the LISA mission should be able to constrain the dark photon mass using extreme mass ratio inspirals in the range $[1.8 \times 10^{-17}, 4.47 \times 10^{-16}]$ eV.

##### 3.Periodic orbits and their gravitational wave radiations in a polymer black hole in loop quantum gravity

**Authors:**Ze-Yi Tu, Tao Zhu, Anzhong Wang

**Abstract:** This article provides a detailed investigation into the motion of the surrounding particles around a polymer black hole in loop quantum gravity (LQG). Using effective potential, the critical bound orbits and innermost stable circular orbits (ISCO) are analyzed. The study finds that the radii and angular momentum of the critical bound orbits decrease with an increase in the parameter $A_\lambda$ which labels the LQG effects, while the energy and angular momentum of the ISCO also decreases with an increase in $A_\lambda$. Based on these findings, we then explore the periodic orbits of the polymer black hole in LQG using rational numbers composed of three integers. Our results show that the rational numbers increase with the energy of particles and decrease with the increase of angular momentum based on a classification scheme. Moreover, compared to a Schwarzschild black hole, the periodic orbits in a polymer black hole in LQG consistently have lower energy, providing a potential method for distinguishing a polymer black hole in LQG from a Schwarzschild black hole. Finally, we also examine the gravitational wave radiations of the periodic orbits of a test object which orbits a supermassive polymer black hole in LQG, which generates intricate GW waveforms that can aid in exhibiting the gravitational structure of the system.

##### 4.Analogue Hawking radiation in a two-level Weyl semimetal system

**Authors:**Bijan Bagchi, Rahul Ghosh, Sauvik Sen}

**Abstract:** In the light of a general scheme of non-Hermitian $\mathcal{PT}$-symmetric Hamiltonian we apply the tetrad-based method to probe the idea of Weyl semimetal black hole analogy. We evaluate the tunneling probability by making use of the conventional null-geodesic approach wherein the associated Hawking radiation is described as a quantum tunneling process across a classically forbidden potential barrier which the event horizon imposes. Our estimate for the tunneling probability is independent of the non-Hermitian parameter that appears in the guiding Hamiltonian.

##### 5.Perturbative Correction to the Average Expansion Rate of Spacetimes with Perfect Fluids

**Authors:**Vincent Comeau

**Abstract:** This paper discusses the leading-order correction induced by cosmological perturbations on the average expansion rate of an expanding spacetime, containing one or many perfect fluids. The calculation is carried out up to the second order in the perturbations, and is kept as general as possible. In particular, no approximation such as a long-wavelength or a short-wavelength limit is invoked, and all three types of perturbations (scalar, vector, and tensor) are considered. First, the average value of the expansion rate is computed over a three-dimensional space-like surface where the total density of the fluids is constant. Then, a formula is derived relating that average value to the one over any other surface, on which a different scalar property of the fluids is constant. Moreover, the general formulas giving the correction to the average expansion rate are applied, in particular, to the case of a spacetime containing a single fluid with a constant equation of state. The sign and the effective equation of state of the corresponding back-reaction effect in the first Friedmann equation are examined.

##### 6.London-like tensor modes of gravitational waves in cosmic string cosmology

**Authors:**Claudio Aravena-Plaza, Víctor Muñoz, Felipe A. Asenjo

**Abstract:** From a classical analysis, we show that gravitational waves in a cosmological medium with equation of state $\omega=-1/3$ can follow a London-like equation, implying that some gravitational wave solutions present a decay for certain wavelengths. This scenario, corresponding to a cosmic string cosmology, induces an attenuation temporal scale on the gravitational wave propagation. We discuss on how these solutions impose a limit on the wavelength of the waves that can propagate, which depends on the type of spatial curvature and the energy density content of this type of cosmology.

##### 7.Quasinormal Modes from EFT of Black Hole Perturbations with Timelike Scalar Profile

**Authors:**Shinji Mukohyama, Kazufumi Takahashi, Keitaro Tomikawa, Vicharit Yingcharoenrat

**Abstract:** The Effective Field Theory (EFT) of perturbations on an arbitrary background geometry with a timelike scalar profile was recently constructed in the context of scalar-tensor theories. In this paper, we use this EFT to study quasinormal frequencies of odd-parity perturbations on a static and spherically symmetric black hole background. Keeping a set of operators that can accommodate shift-symmetric quadratic higher-order scalar-tensor theories, we demonstrate the computation for two examples of hairy black holes, of which one is the stealth Schwarzschild solution and the other is the Hayward metric accompanied by a non-trivial scalar field. We emphasize that this is the first phenomenological application of the EFT, opening a new possibility to test general relativity and modified gravity theories in the strong gravity regime.

##### 8.A synthetic null energy condition

**Authors:**Robert J. McCann

**Abstract:** We give a simplified approach to Kunzinger & S\"amann's theory of Lorentzian length spaces in the globally hyperbolic, regularly localizable case; these provide a nonsmooth framework for general relativity. We close a gap in this setting, by showing consistency of two potentially different notions of timelike geodesic segments used in the literature. We propose a nonsmooth reformulation of Penrose' null energy condition in terms of the timelike curvature-dimension conditions of Cavalletti & Mondino (and Braun), and discuss its consistency and stability properties. This yields new insights even in the smooth setting.

##### 1.Sudden Shock Waves in modified gravity

**Authors:**Ignatios Antoniadis, Spiros Cotsakis, Dimitrios Trachilis

**Abstract:** We construct a generic asymptotic solution for modified gravity near a sudden singularity. This solution contains a fluid source with no equation of state and is function-counting stable, that is it has eleven independent arbitrary functions of the spatial coordinates as dictated by the Cauchy problem of the theory. We further show that near the sudden singularity the solution has a shock wave character with the same number of free functions in the Jordan and Einstein frame.

##### 2.Magnetic black hole in Einstein-Dilaton-Square root nonlinear electrodynamics

**Authors:**S. Habib Mazharimousavi, Kanishk Verma

**Abstract:** Starting from the most general action in Einstein-Dilaton-Nonlinear Electrodynamics (NED) theory, we obtain the field equations. We apply the field equations for the specific NED known as the square root model coupled nonminimally to the dilaton scalar field whose self-interacting is in the Liouville type plus a cosmological constant and solve the field equations. In static spherically symmetric spacetime and a magnetic monopole sitting at the origin, the field equations are exactly solvable provided the integration constants of the solutions and the theory constants appearing in the action are linked through two constraints. As it is known, such an exact solution in the absence of dilaton i.e., gravity coupled to square root NED dosen't exist. Therefore, the presence of the dilaton gives additional freedom to solve the field equations. The obtained spacetime is singular and non-asymptotically flat and depending on the free parameters it may be a black hole or a cosmological object. For the black hole spacetime, we study the thermal stability of the spacetime and show that the black hole is thermally stable provided its size is larger than a critical value.

##### 3.Bounce inflation with a conserved frame of rest

**Authors:**Gustaf Rydbeck

**Abstract:** Some form of approximately exponential inflation is generally assumed to be the origin of our present universe. The inflation is thought to be driven by a scalar field potential where the field first slowly slides along the potential and then comes to a steep slope where the field rapidly falls and then oscillates around zero transforming into particles. The slowly sliding scalar field inflation leads to an exponentially expanding de Sitter space. A scalar field as well as the deSitter space are both Lorentz invariant. Thus no global frame of rest can be established in this scenario, while particle creation requires a preferred frame of rest. Observations of the cosmic microwave background show, when the redshift is corrected for our local velocity, a very even temperature and redshift distribution requiring a global preferred frame of rest. We suggest here that a density dependent equilibrium relation between matter/radiation and a scalar energy density could maintain a preferred frame of rest throughout the bounce and inflation and thereby solve the problem.

##### 4.Mass-Transfer Process of Galactic Compact Binaries

**Authors:**Zi-han Zhang, Bin Liu, Jie Yang

**Abstract:** In this paper we focus on the effect of mass transfer between compact binary stars like neutron star-neutron star (NS-NS) system and neutron star-white dwarf (NS-WD) system. We adopt mass quadrupole formula with post-Newtonian approximation to calculate the gravitational wave (GW) radiation and orbit evolution. Two kinds of mass transfer process are considered here. One is the tidal disruption model where the less dense star orbits into the Roche limit and its mass flows toward to the other star as a beam of incompressible fluid, and the other is common envelope model where we divide the transferring mass into the mass-inflow of envelope and the the envelope itself winding in the Roche lobe of the binary stars. Viewing the envelope as a background, the GW by its spin can be calculated as a pulsar. Assuming a mass-inflow parameter, we eventually obtain the radiation power and corrected gravitational wave form (GWF) templates for different initial mass ratios, which are mainly captured by the inspiral duration and strain and of the GWs.

##### 5.Charged particle dynamics in parabolic magnetosphere around Schwarzschild black hole

**Authors:**Martin Kološ, Misbah Shahzadi, Arman Tursunov

**Abstract:** The study of charged particle dynamics in the combined gravitational and magnetic field can provide important theoretical insight into astrophysical processes around black holes. In this paper, we explore the charged particle dynamics in parabolic magnetic field configuration around Schwarzschild black hole, since the paraboloidal shapes of magnetic field lines around black holes are well motivated by the numerical simulations and supported by observations of relativistic jets. Analysing the stability of bounded orbits and using the effective potential approach, we show the possibility of existence of stable circular off-equatorial orbits around the symmetry axis. We also show the influence of radiation reaction force on the dynamics of charged particles, in particular on the chaoticity of the motion and Poincar\'{e} sections, oscillatory frequencies, and emitted electromagnetic spectrum. Applied to Keplerian accretion disks, we show that in parabolic magnetic field configuration, the thin accretion configurations can be either destroyed or transformed into a thick toroidal structure given the radiation reaction and electromagnetic-disk interactions included. Calculating the Fourier spectra for radiating charged particle trajectories, we find that the radiation reaction force does not affect the main frequency peaks, however, it lowers the higher harmonics making the spectrum more flat and diluted in high frequency range.

##### 6.Gravitational waves from compact binaries to the fourth post-Newtonian order

**Authors:**F. Larrouturou

**Abstract:** The precise knowledge of the gravitational phase of compact binaries is crucial to the data analysis for gravitational waves. Until recently, it was known analytically (for non-spinning systems) up to the 3.5 post-Newtonian (PN) order, i.e. up to the $(v/c)^7$ correction beyond the leading order. If this precision is sufficient for the data analysis of the current generation of detectors, the next ones (notably LISA and ET) may require higher accuracy. Using a post-Newtonian-multipolar-post-Minkowskian matching algorithm, we have pushed the accuracy to the next level, namely the 4PN order. This derivation involved challenging technical issues, due to the appearance of non-physical divergences, that have to be properly regularized, as well as non-linear interaction terms.

##### 1.Constraints on $f(Q)$ logarithmic model using gravitational wave standard sirens

**Authors:**José Antonio Nájera, Carlos Aráoz Alvarado, Celia Escamilla-Rivera

**Abstract:** In this paper, we revise the constraints on the $f(Q)=Q/(8\pi G) - \alpha \ln(Q/Q_0)$, symmetric teleparallel model using local measurements and gravitational waves mock standard sirens. Using observational local SNIa and BAO data and energy conditions, the logarithmic $f(Q)$ model is capable of explaining the cosmic late-time acceleration by geometrical means. This result suggests that the logarithmic symmetric teleparallel model could be a candidate to solve the cosmological constant problem. In the case of the simulated standard siren data, by using the performance of the future ET and LISA detectors, we expect to be able to measure the current Hubble constant $H_0$, and the matter content $\Omega_m$, with a precision better than 1% and 6%, respectively. Furthermore, we explore the predicted $f(Q)$ logarithmic model deviation from the standard GR using ET and LISA mock standard sirens. The ratio $d_L^{\text{gw}}(z)/d_L^{\text{em}}(z)$, which quantifies the deviation from GR gives us a significant deviation higher than 13% at $z=1$, and it continues growing to reach a deviation higher than 18% in its median value. Future standard siren data will be able to quantify the strength of the deviation from GR and hence whether a cosmology like the one implied by this $f(Q)$ model is feasible.

##### 2.Can a variation of Fine Structure Constant influence the fate of Gravitational Collapse?

**Authors:**Soumya Chakrabarti

**Abstract:** We show that it is possible to steer clear of a spacetime singularity during gravitational collapse by considering the time-variation of a fundamental coupling, in this case, the fine structure constant {\alpha}. We study a spherical distribution of cold dark matter coexisting with other fluid elements, collapsing under its own gravity. Dark matter is written as a scalar field interacting with electrically charged matter. This leads to a time variation of {\alpha} and as a consequence, a breakdown of local charge conservation within the sphere. The exterior has no such field and therefore, Einstein's GR and standard equivalence principles remain valid. We derive the lowest possible bound on the collapse of this sphere beyond which there is a bounce and dispersal of most of the accumulated matter. We discuss the critical behavior of the system around this point and show that the bound is connected to a length scale of the order of Planck, introduced in theory for dimensional requirements.

##### 3.Non-spherical sources of Schwarzschild space-time

**Authors:**J. L. Hernández-Pastora, L. Herrera

**Abstract:** While it is known that any spherical fluid distribution may only source the spherically symmetric Schwarzschild space-time, the inverse is not true. Thus, in this manuscript, we find exact axially symmetric and static fluid (interior) solutions to Einstein equations, which match smoothly on the boundary surface to the Schwarzschild (exterior) space-time, even though the fluid distribution is not endowed with spherical symmetry. The solutions are obtained by using the general approach outlined in [1], and satisfy the usual requirements imposed to any physically admissible interior solution. A discussion about the physical and geometric properties of the source is presented. The relativistic multipole moments (RMM) are explicitly calculated in terms of the physical variables, allowing to prove that spherical sources can only match to the Schwarzschild space-time. The complexity of the source is evaluated through the complexity factors. It is shown that there is only one independent complexity factor, as in the spherically symmetric case.

##### 4.Parameter constraints from shadows of Kerr-Newman-dS black holes with cloud strings and quintessence

**Authors:**Wen-Fu Cao, Wen-Fang Liu, Xin Wu

**Abstract:** The motion of photons around the Kerr-Newman-dS black hole surrounded by quintessence and a cloud of strings is investigated. The existence of the Carter constant leads to that of unstable circular photon orbits on a two-dimensional plane not limited to the equatorial plane and unstable spherical photon orbits in the three-dimensional space. These circular or spherical photon orbits can determine two impact parameters, which are used to calculate black hole shadows. For the case of a spherically symmetric nonrotating black hole, the black hole shadow is circular and its size is independent of an observation angle and a plane on which a circular photon orbit exists. The shadow size increases as any one of the parameters involving the cloud of strings, quintessence parameter, and magnitude of quintessential state parameter increases. However, the black hole shadow is dependent on the observation angle when the black hole is spinning and axially symmetric. The shadow is nearly circular when the observation angle decreases to zero for a larger black hole spin. It seems to be more deformable when the black hole spin increases for a larger observation angle. In this case, the shadow size increases as any one of the parameters increases. The curvature radii at the characteristic points increase with the parameters increasing. Based on the Event Horizon Telescope observations of M87*, the constraint of the curvature radius is used to constrain the parameters. For slowly rotating spin black holes, the allowed regions of the parameters including the cosmological constant are given.

##### 5.The cosmological frame principle and cosmic acceleration

**Authors:**Spiros Cotsakis, Jose P. Mimoso, John Miritzis

**Abstract:** We discuss cosmological implications of the frame principle which states that physics is independent of frames. We show that there are frame-independent solutions that are globally stable, suggesting that they represent physically relevant solutions. This result highlights the importance of further investigation into the implications of the cosmological frame principle for cosmological properties that depend on a use of conformal frames.

##### 6.Black hole hairs in scalar-tensor gravity (and lack thereof)

**Authors:**Lodovico Capuano, Luca Santoni, Enrico Barausse

**Abstract:** Scalar-tensor theories are a natural alternative to general relativity, as they may provide an effective dark energy phenomenology on cosmological scales while passing local tests, but their black hole solutions are still poorly understood. Here, we generalize existing no-hair theorems for spherical black holes and specific theories in the scalar-tensor class. We show that shift symmetry prevents the appearance of scalar hairs in rotating (asymptotically flat, stationary and axisymmetric) black holes for all theories in the Horndeski/beyond Horndeski/DHOST classes, but for those with a coupling between the scalar and the Gauss--Bonnet invariant. Our proof also applies to higher dimensions. We also compute the values of the scalar hair charges if shift symmetry and asymptotic flatness are violated by a time growth of the scalar field at infinity, under suitable regularity conditions at the event horizon.

##### 7.Lorentz Violation in Finsler Geometry

**Authors:**Jie Zhu, Bo-Qiang Ma

**Abstract:** Lorentz invariance is one of the foundations of modern physics; however, Lorentz violation may happen from the perspective of quantum gravity, and plenty of studies on Lorentz violation have arisen in recent years. As a good tool to explore Lorentz violation, Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. Here, we simply introduce the mathematics of Finsler geometry. We review the connection between modified dispersion relations and Finsler geometries and discuss the physical influence from Finsler geometry. We review the connection between Finsler geometries and theories of Lorentz violation, such as the doubly special relativity, the standard-model extension, and the very special relativity.

##### 8.Timelike and null geodesics in the Schwarzschild space-time: Analytical solutions

**Authors:**Adam Cieślik, Patryk Mach

**Abstract:** The theory of Schwarzschild geodesics is revisited. Using a theorem due to Weierstrass and Biermann, we derive concise formulas describing all timelike and null trajectories in terms of Weierstrass elliptic functions. The formulation given in this note uses an analogue of the so-called Mino time.

##### 9.Minimally modeled characterization method of postmerger gravitational wave emission from binary neutron star coalescences

**Authors:**Maria Concetta Tringali, Anna Puecher, Claudia Lazzaro, Riccardo Ciolfi, Marco Drago, Bruno Giacomazzo, Gabriele Vedovato, Giovanni Andrea Prodi

**Abstract:** Gravitational waves emitted during the coalescence of binary neutron star systems carry information about the equation of state describing the extremely dense matter inside neutron stars. In particular, the equation of state determines the fate of the binary after the merger: a prompt collapse to black hole, or the formation of a neutron star remnant that is either stable or survives up to a few seconds before collapsing to a black hole. Determining the evolution of a binary neutron star system will therefore place strong constraints on the equation of state. We present a morphology-independent method, developed in the framework of the coherentWaveBurst analysis of signals from ground-based interferometric detectors of gravitational waves. The method characterizes the time-frequency postmerger gravitational-wave emission from a binary neutron star system, and determines whether, after the merger, it formed a remnant neutron star or promptly collapsed to a black hole. We measure the following quantities to characterize the postmerger emission: ratio of signal energies and match of luminosity profile in different frequency bands, weighted central frequency and bandwidth. From these quantities, based on the study of signals simulated through injections of numerical relativity waveforms, we build a statistics to discriminate between the different scenarios after the merger. Finally, we test our method on a set of signals simulated with new models, to estimate its efficiency as a function of the source distance.

##### 1.The Hawking temperature of dynamical black holes via Rindler transformations

**Authors:**Pravin Kumar Dahal, Fil Simovic

**Abstract:** The Vaidya metric serves as a useful model-building tool that captures many essential features of dynamical and/or evaporating black hole spacetimes. Working in a semiclassical setting, we show that in the limit of slow evaporation, a general spherically symmetric metric subject to certain regularity conditions is uniquely described by a linear ingoing Vaidya metric in the near-horizon region. This suggests a universal description of the near-horizon geometry of evaporating black holes in terms of the linear Vaidya metric. We also demonstrate that the linear Vaidya metric can be brought into manifestly conformally static form, allowing us to determine the Hawking temperature associated with the Vaidya background with respect to the conformal vacuum. Since back-reaction is implicitly accounted for, we conclude that slowly evaporating black holes are indeed accurately described by quasistatic sequences of Schwarzschild metrics even when dynamical effects are present.

##### 2.Numerical simulations of black hole-neutron star mergers in scalar-tensor gravity

**Authors:**Sizheng Ma, Vijay Varma, Leo C. Stein, Francois Foucart, Matthew D. Duez, Lawrence E. Kidder, Harald P. Pfeiffer, Mark A. Scheel

**Abstract:** We present a numerical-relativity simulation of a black hole - neutron star merger in scalar-tensor (ST) gravity with binary parameters consistent with the gravitational wave event GW200115. In this exploratory simulation, we consider the Damour-Esposito-Farese extension to Brans-Dicke theory, and maximize the effect of spontaneous scalarization by choosing a soft equation of state and ST theory parameters at the edge of known constraints. We extrapolate the gravitational waves, including tensor and scalar (breathing) modes, to future null-infinity. The numerical waveforms undergo ~ 22 wave cycles before the merger, and are in good agreement with predictions from post-Newtonian theory during the inspiral. We find the ST system evolves faster than its general-relativity (GR) counterpart due to dipole radiation, merging a full gravitational-wave cycle before the GR counterpart. This enables easy differentiation between the ST waveforms and GR in the context of parameter estimation. However, we find that dipole radiation's effect may be partially degenerate with the NS tidal deformability during the late inspiral stage, and a full Bayesian analysis is necessary to fully understand the degeneracies between ST and binary parameters in GR.

##### 3.Laws of thermodynamic equilibrium through relativistic thermodynamics

**Authors:**Bibhas Ranjan Majhi

**Abstract:** Using Israel-Stewart formalism for the description of thermodynamics of an arbitrary relativistic fluid we propose generalization of Tolman-Ehrenfest relation and Klein's law on a general background spacetime. The first relation is a consequence of thermal equilibrium only of a non-viscous fluid, while the latter one is reflection of only no-diffusion condition with or without viscosity. Interestingly, both the relations are obtained independently through the imposition of respective equilibrium conditions and also valid in presence of particular dissipative processes in the fluid. For a spacetime with a global timelike Killing vector, these two general relations boil down to standard forms.

##### 4.Spin-0 fields and the NP-constants close to spatial infinity in Minkowski spacetime

**Authors:**Edgar Gasperin, Rafael Pinto

**Abstract:** The NP constants of the spin-0 field propagating in Minkowski spacetime are computed close to spatial and null infinity by means of Friedrich's $i^0$-cylinder. Assuming certain regularity condition on the initial data ensuring that the field extends analytically to the critical sets, it is shown that the NP constants at future $\mathscr{I}^{+}$ and past null infinity $\mathscr{I}^{-}$ are independent of each other. In other words, the classical NP constants at $\mathscr{I}^{\pm}$ stem from different parts of the initial data given on a Cauchy hypersurface. In contrast, it is shown that, using a slight generalisation of the classical NP constants, the associated quantities ($i^0$-cylinder NP constants) do not require the regularity condition being satisfied and give rise to conserved quantities at $\mathscr{I}^{\pm}$ that are determined by the same piece of initial data which, in turn, correspond to the terms controlling the regularity of the field. Additionally, it is shown how the conservation laws associated to the NP constants can be exploited to construct, in flat space, heuristic asymptotic-system expansions which are sensitive to the logarithmic terms at the critical sets.

##### 5.Birth of baby universes from gravitational collapse in a modified-gravity scenario

**Authors:**Andreu Masó-Ferrando, Nicolas Sanchis-Gual, José A. Font, Gonzalo J. Olmo

**Abstract:** We consider equilibrium models of spherical boson stars in Palatini $f(\mathcal{R})=\mathcal{R}+\xi \mathcal{R}^2$ gravity and study their collapse when perturbed. The Einstein-Klein-Gordon system is solved using a recently established correspondence in an Einstein frame representation. We find that, in that frame, the endpoint is a nonrotating black hole surrounded by a quasi-stationary cloud of scalar field. However, the dynamics in the $f(\mathcal{R})$ frame is dramatically different. The innermost region of the collapsing object exhibits the formation of a finite-size, exponentially-expanding $\textit{ baby universe}$ connected with the outer (parent) universe via a minimal area surface (a throat or umbilical cord). Our simulations indicate that this surface is at all times hidden inside a horizon, causally disconnecting the baby universe from observers above the horizon. The implications of our findings in other areas of gravitational physics are also discussed.

##### 6.Summing over Non-singular Paths in Quantum Cosmology

**Authors:**Hiroki Matsui

**Abstract:** In this paper, we provide the DeWitt propagator and its wave function in quantum cosmology using the path integral formulation of quantum gravity. The DeWitt boundary condition is introduced as a way of avoiding the Big Bang singularity by positing that the wave function of the universe vanishes near the Big Bang. However, there is currently no clear definition of the DeWitt boundary condition in the path integral formulation. To address this issue, we employ the image method, which eliminates singular paths in the forbidden region of an infinite potential and apply this method to quantum cosmology based on the Batalin-Fradkin-Vilkovisky formulation of the path integral and Picard-Lefschetz theory. We investigate the validity of the image method, and specifically, find that this method is appropriate only when the potential exhibits symmetry with respect to the boundary. Then, we show that the DeWitt propagator and the DeWitt wave function derived the image method are consistent with solutions of the Wheeler-DeWitt equation for specific models of quantum cosmology.

##### 7.Birth and death of entanglement between two accelerating Unruh-DeWitt detectors coupled with a scalar field

**Authors:**Dawei Wu, Shan-Chang Tang, Yu Shi

**Abstract:** We consider two accelerating Unruh-DeWitt detectors coupled linearly or quadratically with a scalar field. We show that entanglement can be created by acceleration, and is divergent only when the two detectors coincide. For linear coupling, entanglment decreases monotonically with the increase of acceleration. For quadratic coupling, entanglement behaves non-monotonically.

##### 8.Cosmic evolution under the quantization of real scalar field

**Authors:**Subhayan Maity, Sujayita Bakra

**Abstract:** General theory of relativity is the most popular theory to describe the dynamics of a system (especially the Universe) under gravity. In this framework, the solution of Einstein field equation under curved space-time yields the cosmic evolution equation. However the evolutionary dynamics of the Universe may also be obtained from the other aspects like thermodynamics, classical Lagrangian dynamics, symmetry analysis(Noether, Lie ) etc. This work provides an different approach to obtain the cosmic evolution equation from the quantization of the cosmic fluid under gravity.

##### 9.The Return of GOLUM: Improving Distributed Joint Parameter Estimation for Strongly-Lensed Gravitational Waves

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

**Abstract:** Owing to the forecasted improved sensitivity of ground-based gravitational-wave detectors, new research avenues will become accessible. This is the case for gravitational-wave strong lensing, predicted with a non-negligible observation rate in the coming years. However, because one needs to investigate all the event pairs in the data, searches for strongly-lensed gravitational waves are often computationally heavy, and one faces high false-alarm rates. In this paper, we present upgrades made to the \GOLUM software, making it more reliable while increasing its speed by re-casting the look-up table, imposing a sample control, and implementing symmetric runs on the two lensed images. We show how the recovered posteriors have improved coverage of the parameter space and how we increase the pipeline's stability. Finally, we show the results obtained by performing a joint analysis of all the events reported until the GWTC-3 catalog, finding similar conclusions to the ones presented in the literature.

##### 10.Initial conditions problem in cosmological inflation revisited

**Authors:**David Garfinkle, Anna Ijjas, Paul J. Steinhardt

**Abstract:** We present first results from a novel numerical relativity code based on a tetrad formulation of the Einstein-scalar field equations combined with recently introduced gauge/frame invariant diagnostics indicating that inflation does not solve the homogeneity and isotropy problem beginning from generic initial conditions following a big bang.

##### 11.Parametrized black holes: Scattering investigation

**Authors:**Renan B. Magalhães, Luiz C. S. Leite, Luís C. B. Crispino

**Abstract:** We study the scattering of light-like geodesics and massless scalar waves by a static Konoplya-Zhidenko black hole, considering the case that the parametrized black hole solution contains a single deformation parameter. By performing a geodesic analysis, we compute the classical differential scattering cross section and probe the influence of the deformation parameter on null trajectories. Moreover, we investigate the propagation of a massless scalar field in the vicinity of the static Konoplya-Zhidenko black hole and use the plane waves formalism to compute the differential scattering cross section. We confront our numerical results in the backward direction with the glory approximation, finding excellent agreement. We compare the results for the deformed black hole with the Schwarzschild case, finding that the additional parameter has an important role in the behavior of the scattering process for moderate-to-high scattering angles.

##### 12.On the irrelevance of the scrambling power of gravity for black hole radiation

**Authors:**Xuan-Lin Su, Alioscia Hamma, Antonino Marciano

**Abstract:** Black holes are a recently observed theoretical prediction of General Relativity, characterized by event horizons, from which information cannot escape. Examined through the lenses of quantum mechanics, they can radiate at a definite temperature inverse to their mass and horizon radius. Hawking radiation, whose spectrum was calculated considering particles scattering off black holes, is connected to the paradox of the loss of information falling into them. Information can become non-fungible, due to scrambling. We demonstrate this feature not to be restricted to curved space-times: soft radiation scattering in a flat space-time does scramble information as well. To this end, we compute the scrambling of information through the tripartite mutual information in a scattering process off a black hole and compare it with the flat space-time analog. We show that the scrambling power of the gravitational field of a black hole is negligible with respect to the scrambling power of flat space-time.

##### 1.Gravitationally modulated quantum correlations: Discriminating classical and quantum models of ultra-compact objects with Bell nonlocality

**Authors:**Luciano Petruzziello, Fabrizio Illuminati

**Abstract:** We investigate the relation between quantum nonlocality and gravity at the astrophysical scale, both in the classical and quantum regimes. Considering particle pairs orbiting in the strong gravitational field of ultra-compact objects, we find that the violation of Bell inequality acquires an angular modulation factor that strongly depends on the nature of the gravitational source. We show how such gravitationally-induced modulation of quantum nonlocality readily discriminates between black holes (both classical and inclusive of quantum corrections) and string fuzzballs, i.e., the true quantum description of ultra-compact objects according to string theory. These findings promote Bell nonlocality as a potentially key tool in comparing different models of classical and quantum gravity and putting them to the test.

##### 2.Disformal symmetry in the Universe: mimetic gravity and beyond

**Authors:**Guillem Domènech, Alexander Ganz

**Abstract:** Symmetries play an important role in fundamental physics. In gravity and field theories, particular attention has been paid to Weyl (or conformal) symmetry. However, once the theory contains a scalar field, conformal transformations of the metric can be considered a subclass of a more general type of transformation, so-called disformal transformation. Here, we investigate the implications of pure disformal symmetry in the Universe. We derive the form of general disformal invariant tensors from which we build the most general disformal invariant action. We argue that, in cosmology, disformal symmetry amounts to require that the lapse function is fully replaced by a (time-like) scalar field at the level of the action. We then show that disformal symmetry is in general an exactly equivalent formulation of general mimetic gravity. Lastly, we go beyond mimetic gravity and find that a particular class of invariance leads to seemingly Ostrogradski-like (with higher derivatives) Lagrangians, which are nevertheless absent of Ostrogradski ghosts in a cosmological background, despite having an additional degree of freedom. We also propose an application of our formalism to find new invertible disformal transformations, where the coefficient involves higher derivatives and curvature, further expanding the theory space of scalar-tensor theories.

##### 3.Attractor Solutions in Interacting Dark Energy Models

**Authors:**Yousef Bisabr

**Abstract:** We investigate a cosmological model in which dark energy, represented by a quintessential scalar field, is coupled to a dark-matter perfect fluid in the spatially flat Friedmann-Robertson-Walker Universe. This allows an energy exchange in the dark sector which could happen both at early times before recombination era or at late times. We use the coupling function $Q=\gamma\rho_{dm}\dot{\varphi}$ which is induced by conformal transforming scalar-tensor and $f(R)$ gravity theories to Einstein frame. It is argued that there is a connection between this coupling function and $Q\propto \rho_{dm}H$. A dynamical analysis is used to show that there are early- and late-time attracting solutions for which the system evolves for a wide range of initial conditions. These attractors generalize the scaling solutions which have been already found in the non-interacting case.

##### 4.Casimir-Yang-Mills wormholes in $D=2+1$

**Authors:**A. C. L. Santos, C. R. Muniz, R. V. Maluf

**Abstract:** This study presents new three-dimensional traversable wormhole solutions sourced by the Casimir density and pressure related to the quantum vacuum fluctuations in Yang-Mills theory. First, we analyze the noninteracting Casimir effect with an arbitrary state parameter $\omega$ and determine a simple constant wormhole shape function. We introduce a new methodology for deforming the state parameter and find well-behaved redshift functions. The wormhole can be interpreted as a legitimate Casimir wormhole with an expected average state parameter of $\omega=2$. Then, we investigate the curvature properties, energy conditions, and stability of the wormholes, finding that they are stable only if the radius exceeds a specific value near the throat. Furthermore, we discover a new family of traversable wormhole solutions sourced by the quantum vacuum fluctuations of interacting (confined) Yang-Mills fields with a more complex shape function. Deforming the effective state parameter similarly, we obtain well-behaved redshift functions and wormhole solutions that depend on relevant parameters of the system. Notably, higher string tension results in a larger throat radius, potentially driven by an attempt to deconfine gluons and stretch the wormhole.

##### 1.Testing the first law of black hole mechanics with gravitational waves

**Authors:**Chao-Wan-Zhen Wang, Fu-Wen Shu

**Abstract:** GW191219\_163120 is a gravitational wave signal that is believed to have originated from a neutron star-black hole (NSBH) coalescence with an extreme mass ratio. In this work, we use data of GW191219\_163120 from LIGO and Virgo to test the first law of black hole mechanics by considering the neutron star as a perturbation to the black hole before the merger, and the remnant black hole as a stationary black hole after the merger. Our results demonstrate consistency with the first law of black hole mechanics, with an error level of about 6\% at 68\% credibility and 10\% at 95\% credibility. We also find that the higher the mass ratio of the gravitational wave source, the more consistent our results are with the first law of black hole mechanics. Overall, our study sheds light on the nature of NSBH coalescences and their implications for black hole mechanics.

##### 2.Spatially homogeneous solutions of vacuum Einstein equations in general dimensions

**Authors:**Yuichiro Sato, Takanao Tsuyuki

**Abstract:** We find three new exact solutions of the vacuum Einstein equations without cosmological constant in more than three dimensions. We consider globally hyperbolic spacetimes in which almost abelian Lie groups act on the spaces isometrically and simply transitively. We give left-invariant metrics on the spaces and solve Ricci-flat conditions of the spacetimes. In the four-dimensional case, our solutions correspond to the Bianchi type II vacuum solution. By our results and previous studies, all spatially homogeneous solutions whose spaces have zero-dimensional moduli spaces of left-invariant metrics are found. For the simplest solution, we show that each of the spatial dimensions cannot expand or contract simultaneously in the late-time limit.

##### 3.Buchdahl Bound and Geometrical Virial Theorem

**Authors:**Naresh Dadhich, Rituparno Goswami, Chevarra Hansraj

**Abstract:** Buchdahl stars are defined by the saturation of the Buchdahl bound; the gravitational potential felt by a radially falling particle is less than equal to 4/9. An interesting alternative characterization is given by gravitational energy being half of non-gravitational energy. With insightful identification of the former with kinetic and the latter with potential energy, it has been recently argued that the equilibrium of a Buchdahl star may be governed by the Virial theorem. In this essay, we provide a purely geometric version of this theorem and thereby of the Buchdahl star characterization. We show that a collapsing star maintaining the Virial equilibrium must expel energy via heat flux, appearing in the exterior as Vaidya radiation, and it escapes getting trapped into a black hole.

##### 4.Covariant Canonical Gauge Theory of Classical Gravitation for Scalar, Vector, and Spin-1/2 Particle Fields

**Authors:**David Vasak, Jürgen Struckmeier

**Abstract:** The framework of the Covariant Canonical Gauge theory of Gravity (CCGG) is described in detail. CCGG emerges naturally in the Palatini formulation, where the vierbein and the spin connection are independent fields. Neither torsion nor non-metricity are excluded. The manifestly covariant gauge process is based on canonical transformations in the De Donder-Weyl Hamiltonian formalism, starting from a small number of basic postulates. Thereby, the original system of matter fields in flat spacetime, represented by non-degenerate Hamiltonian densities, is amended by spacetime fields. The coupling of matter and spacetime fields leaves the action integral of the combined system invariant under active local Lorentz transformations and passive diffeomorphisms, aka Principle of General Relativity. We consider the Klein-Gordon, Maxwell-Proca, and Dirac fields and derive the corresponding equations of motion. Albeit the coupling of the given matter fields to the gauge fields are unambiguously determined by CCGG, the dynamics of the free gauge fields must be postulated based on physical reasoning. Our choice allows to derive Poisson-like equations of motion also for curvature and torsion. The latter is proven to be totally anti-symmetric. The affine connection is a function of the spin connection and vierbein fields. Requesting the spin connection to be anti-symmetric gives naturally metric compatibility. The canonical equations combine to an extension of the Einstein-Hilbert action with a quadratic Riemann-Cartan concomitant that endows spacetime with inertia. Moreover, a non-degenerate, quadratic version of the free Dirac Lagrangian is deployed. When coupled to gravity, the Dirac equation is endowed with an emergent mass parameter, a curvature-dependent mass correction, and novel interactions between particle spin and spacetime torsion.

##### 5.Correction to Lagrangian for Bouncing Cosmologies in $f(Q)$ Gravity

**Authors:**Gaurav N. Gadbail, Ameya Kolhatkar, Sanjay Mandal, P. K. Sahoo

**Abstract:** Symmetric teleparallel gravity offers to reformulate the gravitational formalism without the presence of curvature and torsion with the help of non-metricity tensors. Interestingly, Symmetric teleparallel gravity can be formulated equivalently to teleparallel gravity or general relativity for an appropriate setup. In this study, our aim lies in exploring the bouncing cosmologies as an alternative to the initial singularity of the Universe in the background of modified symmetric teleparallel gravity. To explore this, we adopt the reconstruction technique to present the possible reconstructed Lagrangian for various cosmological bouncing solutions in a flat Friedmann-Lema\^itre-Robertson-Walker spacetime with a perfect fluid matter distribution. We study the reconstructed gravitational Lagrangians, which are capable of reproducing analytical solutions for \textit{symmetric bounce}, \textit{super-bounce}, \textit{oscillatory bounce}, \textit{matter bounce}, and \textit{exponential bouncing} model settings. Further, we examine the dark energy profiles of the models using reconstructed Lagrangians. In addition, we found that an additional term arises in each reconstructed Lagrangian compared to general relativity (GR). That extra term corrected the background GR to present bouncing cosmology in modified gravity. These newly motivated cosmological models may have an effect on gravitational phenomena at other cosmological scales.

##### 6.Regge Pole approach to black hole spectral instability

**Authors:**Theo Torres

**Abstract:** The quasi-normal mode (QNM) spectrum of black holes is unstable under small perturbation of the potential and has observational consequences in time signals. Such signals might be experimentally difficult to observe and probing this instability will be a technical challenge. Here we investigate the spectral instability of time-independent data. This leads us to study the Regge Poles (RP), the counterparts to the QNMs in the complex angular momentum plane. We present evidence that the RP spectrum is unstable but that not all overtones are affected equally by this instability. Furthermore, the RP spectrum appears somehow more robust than its QNM counterpart. In addition, we reveal that behind this spectral instability lies an underlying structure. The RP spectrum is perturbed in such a way that one can still recover stable scattering quantities using the complex angular momentum approach. We argue that physical stability might be the root of the superior robustness of the RP spectrum.

##### 7.General mass formula for charged Kerr-AdS black holes

**Authors:**Yunjiao Gao, Sijie Gao

**Abstract:** It is well-known that the mass of a non-asymptotically flat spacetime cannot be uniquely defined. A reasonable definition of mass for the Kerr-AdS black hole has been found and widely used in studying black hole thermodynamics. However, the derivation usually needs a background subtraction to eliminate the divergence. It is also unknown whether this formula can be extended to a more general form. In this paper, we provide a more straightforward derivation for the mass formula, only demanding that the first law of black hole thermodynamics and Smarr formula are satisfied. We first make use of the Iyer-Wald formalism to derive a first law of charged Kerr-AdS black hole in the extended phase space. However, this mass is obviously not integrable. We then modify the coefficients of the first law to make the mass integrable. Finally, by applying the scaling argument to the modified first law, we obtain the Smarr formula, i.e., the explicit form of the mass. Remarkably, our mass formula contains a free parameter and when it is set to zero, we recover the familiar mass $M/\Xi^2$ in the literature. Moreover, by making use of the gauge freedom of the Killing vector field $\ppa{t}{a}$, we find a favorite parameter $t'$ which just gives the first law and makes the mass integrable. The mass also satisfies the Smarr formula and takes the form $M/\Xi^{3/2}$. To the best of our knowledge, this is a new mass formula and could have important applications in future studies.

##### 8.Quantum avoidance of Gödel's closed timelike curves

**Authors:**Zhe Zhao, Leonardo Modesto

**Abstract:** In a large class of nonlocal as well as local higher derivative theories minimally coupled to the matter sector, we investigate the exactness of two different classes of homogeneous G\"{o}del-type solutions, which may or may not allow closed time-like curves (CTC). Our analysis is limited to spacetimes solving the Einstein's EoM, thus we can not exclude the presence of other G\"{o}del-type solutions solving the EoM of local and nonlocal higher derivative theories but not the Einstein's EoM.It turns out that the homogeneous G\"{o}del spacetimes without CTC are basically exact solutions for all theories, while the metrics with CTC are not exact solutions of (super-)renormalizable local or nonlocal gravitational theories. Hence, the quantum renormalizability property excludes theories suffering of the G\"{o}del's causality violation. We also comment about nonlocal gravity non-minimally coupled to matter. In this class of theories, all the G\"{o}del's spacetimes, with or without CTC, are exact solutions at classical level. However, the quantum corrections, although perturbative, very likely spoil the exactness of such solutions. Therefore, we can state that the G\"{o}del's Universes with CTC and the super-renormalizability are mutually exclusive.

##### 9.Vacua in locally de Sitter cosmologies

**Authors:**Vladimir Toussaint, Jorma Louko

**Abstract:** We analyse the response of a comoving local quantum probe, modelled as an Unruh-DeWitt detector coupled to a massive scalar field, in (1+1)-dimensional spatially homogeneous locally de Sitter cosmologies with compact spatial sections, allowing for the scale factor hyperbolic cosine, hyperbolic sine, and exponential evolution laws, as inherited from different local foliations of the de Sitter geometry. For the sinh and exp scale factors, we consider adiabatic vacua in the past, identifying an ambiguity due to a massive zero mode, while for the cosh and sinh expansion laws, we consider large momentum adiabatic vacua and states induced from the Euclidean vacuum; for the latter, we also evaluate the expectation value of the field's stress-energy tensor. Numerical plots are given in selected parameter regimes.

##### 10.Circular motion and chaos bound of a charged particle near charged 4D Einstein-Gauss-Bonnet-AdS black holes

**Authors:**Jiayu Xie, Jie Wang, Bing Tang

**Abstract:** We investigate the circular motion and chaos bound of a charged particle near 4D charged AdS black holes in Einstein-Gauss-Bonnet gravity theory. By means of the Jacobian matrix, the analytical form of the Lyapunov exponent of the charged particle is constructed, which satisfies the upper bound when it is on the event horizon. By further expanding the Lyapunov exponent near the horizon and investigating a 4D charged Einstein-Gauss-Bonnet-AdS black hole with different Gauss-Bonnet coupling constant, we find that it has some specific values to determine whether a violation of chaos bound. Besides, we find that in contrast to the static equilibrium, the circular motion of charged particle can have a larger Lyapunov exponent due to the existence of angular momentum. Moreover, we show that the black hole gets closer to the extremal state as the Gauss-Bonnet coupling constant increases, and the bound is more easily violated. In addition, the range of particle charge that may violate the chaotic bound are found for different Gauss-Bonnet coupling constants. The results show that as the GB coupling parameter increases, the value of particle charge required to satisfy the violation of the chaos bound is even smaller.

##### 1.Holographic realization of constant roll inflation and dark energy: An unified scenario

**Authors:**Shin'ichi Nojiri, Sergei D. Odintsov, Tanmoy Paul

**Abstract:** Based on generalized holographic formalism, we establish a holographic realization of constant roll inflation during the early universe, where the corresponding cut-off depends on the Hubble parameter and its derivatives (up to the second order). The viability of this holographic constant roll inflation with respect to the Planck data in turn puts a certain bound on the infrared cut-off at the time of horizon crossing. Such holographic correspondence of constant roll inflation is extended to the scenario where the infrared cut-off is corrected by the ultraviolet one, which may originate due to quantum effects. Besides the mere inflation, we further propose the holographic realization of an $unified$ cosmic scenario from constant roll inflation (at the early time) to the dark energy era (at the late time) with an intermediate radiation dominated era followed by a Kamionkowski like reheating stage. In such a unified holographic scenario, the inflationary quantities (like the scalar spectral index and the tensor-to-scalar ratio) and the dark energy quantities (like the dark energy EoS parameter and the present Hubble rate) prove to be simultaneously compatible with observable constraints for suitable ranges of the infrared cut-off and the other model parameters. Moreover the curvature perturbations at super-Hubble scale prove to be a constant (with time) during the entire cosmic era, which in turn ensures the stability of the model under consideration.

##### 2.Global Existence and Completeness of Classical Solutions in Einstein-Klein-Gordon System in Higher Dimensions

**Authors:**Mirda Prisma Wijayanto, Fiki Taufik Akbar, Bobby Eka Gunara

**Abstract:** In this paper we study the global existence and completeness of classical solutions of gravity coupled a scalar field system called Einstein-Klein-Gordon system in higher dimensions. We introduce a new ansatz function to reduce the problem into a single first-order integro-differential equation. Then, we employ the contraction mapping in the appropriate Banach space. Using Banach fixed theorem, we show that there exists a unique fixed point, which is the solution of the theory. For a given initial data, we prove the existence of both local and global classical solutions. We also study the completeness properties of the spacetimes. Here, we introduce a mass-like function for $D\geq 4$ in Bondi coordinates. The completeness of spacetimes along the future directed time-like lines outward to a region which resembles the event horizon of the black hole.

##### 3.Standard quantum field theory from entangled relativity

**Authors:**Olivier Minazzoli

**Abstract:** Despite its non-linear form, entangled relativity possesses both general relativity and standard quantum field theory in a specific (but generic) limit. On one side it means that the theory is consistent with our current understanding of elementary physics. But on the other side it means that our current understanding might actually just be approximately valid: and this, surprisingly, goes for both \textit{general relativity} and standard quantum field theory together.

##### 4.TEOBResumS: Analytic systematics in next-generation of effective-one-body gravitational waveform models for future observations

**Authors:**Alessandro Nagar, Piero Rettegno, Rossella Gamba, Angelica Albertini, Sebastiano Bernuzzi

**Abstract:** The success of analytic waveform modeling within the effective-one-body (EOB) approach relies on the precise understanding of the physical importance of each technical element included in the model. The urgency of constructing progressively more sophisticated and complete waveform models (e.g. including spin precession and eccentricity) partly defocused the research from a careful comprehension of each building block (e.g. Hamiltonian, radiation reaction, ringdown attachment). Here we go back to the spirit of the first EOB works. We focus first on nonspinning, quasi-circular, black hole binaries and analyze systematically the mutual synergy between numerical relativity (NR) informed functions and the high post-Newtonian corrections (up to 5PN) to the EOB potentials. Our main finding is that it is essential to correctly control the noncircular part of the dynamics during the late plunge up to merger. When this happens, either using NR-informed non-quasi-circular corrections to the waveform (and flux) or high-PN corrections in the radial EOB potentials $(D,Q)$, it is easy to obtain EOB/NR unfaithfulness $\sim 10^{-4}$ with the noise of either Advanced LIGO or 3G detectors. We then improve the {\tt TEOBResumS-GIOTTO} waveform model for quasi-circular, spin-aligned binaries black hole binaries. We obtain maximal EOB/NR unfaithfulness ${\bar{\cal F}}^{\rm max}_{\rm EOBNR}\sim 10^{-3}$ (with Advanced LIGO noise and in the total mass range $10-200M_\odot$) for the dominant $\ell=m=2$ mode all over the 534 spin-aligned configurations available through the Simulating eXtreme Spacetime catalog. The model performance, also including higher modes, is then explored using NR surrogate waveform models to validate {\tt TEOBResumS-GIOTTO} up to mass ratio $m_1/m_2=15$.

##### 5.Modified General Relativity and dark matter

**Authors:**Gary Nash

**Abstract:** Modified General Relativity (MGR) is the natural extension of General Relativity (GR). MGR explicitly uses the smooth regular line element vector field $(\bm{X},-\bm{X}) $, which exists in all Lorentzian spacetimes, to construct a connection-independent symmetric tensor that represents the energy-momentum of the gravitational field. It solves the problem of the non-localization of gravitational energy-momentum in GR, preserves the ontology of the Einstein equation, and maintains the equivalence principle. The line element field provides MGR with the extra freedom required to describe dark energy and dark matter. An extended Schwarzschild solution for the matter-free Einstein equation of MGR is developed, from which the Tully-Fisher relation is derived, and the gravitational energy density is calculated. The mass of the invisible matter halo of galaxy NGC 3198 calculated with MGR is identical to the result obtained from GR using a dark matter profile. Although dark matter in MGR is described geometrically, it has an equivalent representation as a particle with the property of a vector boson or a pair of fermions; the geometry of spacetime and the quantum nature of matter are linked together by the unit line element covectors that belong to both the Lorentzian metric and the spin-1 Klein-Gordon wave equation. The three classic tests of GR provide a comparison of the theories in the solar system and several parts of the cosmos. MGR provides the flexibility to describe inflation after the Big Bang and galactic anisotropies.

##### 6.Novel charged black hole solutions of Born-Infeld type: General properties, Smarr formula and Quasinormal frequencies

**Authors:**L. Balart, S. Belmar-Herrera, G. Panotopoulos, Á. Rincón

**Abstract:** We investigate two novel models of charged black holes in the framework of non-linear electrodynamics of Born-Infeld type. In particular, starting from two concrete Lagrangian densities, the corresponding metric potentials, the electric field, the Smarr formula and finally, the (scalar) quasinormal modes are computed for each model. Our findings show that although the models look very similar, their quasinormal spectra are characterized by certain differences.

##### 7.Comment on "Observational Evidence for Cosmological Coupling of Black Holes and its Implications for an Astrophysical Source of Dark Energy"

**Authors:**Tobias Mistele

**Abstract:** It was recently claimed that black holes can explain the accelerated expansion of the universe. Here we point out that this claim is based on a confusion about the principle of least action, undermining the link between black holes and dark energy.

##### 1.On two body gravitational scattering within perturbative gravit

**Authors:**Boris Latosh, Anton Yachmenev

**Abstract:** We discuss an alternative approach to studying the low energy limit of quantum general relativity. We investigate the low energy limit of a scattering cross-section for two massive scalar particles. Unlike calculations involving the reconstruction of the gravitational potential, our approach avoids ambiguities and is applicable in any frame. Our results are in agreement with both relativistic and non-relativistic calculations. The non-analytic parts of scattering amplitudes that are dominant in the low energy limit also contribute to the cross-section and provide a way to separate the lading order corrections.

##### 2.Energy extraction from rotating regular black hole via magnetic reconnection

**Authors:**Zhen Li, Xiao-Kan Guo, Faqiang Yuan

**Abstract:** Recently, it has been demonstrated that magnetic reconnection processes in the ergosphere of a Kerr black hole can provide us with a promising mechanism for extracting the rotational energy from it. In this paper, we study the energy extraction from the the newly proposed rotating regular black holes via this magnetic reconnection mechanism. This novel rotating regular black hole has an exponential convergence factor $e^{-k/r}$ on the mass term characterized by the regular parameter $k$ in the exponent. We explore the effects of this regular parameter on the magnetic reconnection as well as other critical parameters determining the magnetic reconnection process. The parameter spaces allowing energy extraction to occur are investigated. The power, efficiency and the power ratio to the Blandford-Znajek mechanism are studied. The results show that the regularity of the rotating black hole has significant effects on the energy extraction via the magnetic reconnection mechanism.

##### 3.Spin-Gravity Coupling in a Rotating Universe

**Authors:**Bahram Mashhoon, Masoud Molaei, Yuri N. Obukhov

**Abstract:** The coupling of intrinsic spin with the nonlinear gravitomagnetic fields of Goedel-type spacetimes is studied. We work with Goedel-type universes in order to show that the main features of spin-gravity coupling are independent of causality problems of the Goedel universe. The connection between the spin-gravitomagnetic field coupling and Mathisson's spin-curvature force is demonstrated in the Goedel-type universe. That is, the gravitomagnetic Stern--Gerlach force due to the coupling of spin with the gravitomagnetic field reduces in the appropriate correspondence limit to the classical Mathisson spin-curvature force.

##### 4.Anisotropic power-law inflation for a generalized model of two scalar and two vector fields

**Authors:**Tuan Q. Do, W. F. Kao

**Abstract:** Cosmological implication of a generalized model of two scalar and two vector fields, in which both scalar fields are non-minimally coupled to each vector field, is studied in this paper. In particular, we will seek an anisotropic power-law inflationary solution to this model. Furthermore, the stability of the obtained solution will be examined by using the dynamical system approach. As a result, we will show that this solution turns out to be stable and attractive during the inflationary phase as expected due to the existence of the unusual couplings between two scalar and two vector fields. Remarkably, we will point out that the existence of phantom field will lead to an instability of the corresponding anisotropic power-law inflation.

##### 5.Complexity factor Parametrization for Traversable Wormholes

**Authors:**Subhra Bhattacharya, Subhasis Nalui

**Abstract:** It is known that static traversable wormhole in Einstein gravity is supported by matter that violates null energy conditions (NEC). Essentially such wormhole will be characterised by a central throat with anisotropic matter lining the throat that violates NEC. This in turn provides viable geometry for the wormhole to sustain. In 2018, L. Herrera introduced a new classification for spherically symmetric bodies called ``complexity factor". It was proposed that a spherically symmetric non trivial geometry can be classified as complex or non-complex based on the nature of the inhomogeneity and anisotropy of the stress energy tensors with only homogeneous and isotropic matter distribution leading to null complexity. Mathematically there was also another way of obtaining zero complexity geometry. In this context since static traversable wormhole by default is characterised by anisotropic and inhomogeneous matter stress tensors, the question we answer is whether it is possible to obtain zero complexity class of wormholes supported by exotic matter.

##### 6.Dynamic behaviours of black hole phase transitions near quadruple points

**Authors:**Jiayue Yang, Robert B. Mann

**Abstract:** Treating the horizon radius as an order parameter in a thermal fluctuation, the free energy landscape model sheds light on the dynamic behaviour of black hole phase transitions. Here we carry out the first investigation of the dynamics of the recently discovered multicriticality in black holes. We specifically consider black hole quadruple points in D=4 Einstein gravity coupled to non-linear electrodynamics. We observe thermodynamic phase transitions between the four stable phases at a quadruple point as well as the weak and strong oscillatory phenomena by numerically solving the Smoluchowski equation describing the evolution of the probability distribution function. We analyze the dynamic evolution of the different phases at various ensemble temperatures and find that the probability distribution of a final stationary state is closely tied to the structure of its off-shell Gibbs free energy.

##### 7.Tests of modified gravitational wave propagations with gravitational waves

**Authors:**Tao Zhu, Wen Zhao, Jian-Ming Yan, Cheng Gong, Anzhong Wang

**Abstract:** Any violation of the fundamental principles of general relativity (GR), including the violations of the equivalence principle and parity/Lorentz symmetries, could induce possible derivations in the gravitational wave (GW) propagations so they can be tested/constrained directly by the GW data. In this letter, we present a universal parametrization for characterizing possible derivations from GW propagations in GR. This parametrization provides a general framework for exploring possible modified GW propagations arising from a large number of modified theories of gravity. With this parameterization, we construct the modified GW waveforms generated by the coalescence of compact binaries with the effects of the gravitational parity/Lorentz violations, then analyze the open data of compact binary merging events detected by LIGO/Virgo/KAGRA collaboration. We do not find any signatures of gravitational parity/Lorentz violations, thereby allowing us to place several of the most stringent constraints on parity/Lorentz violations in gravity and a first constraint on the Lorentz-violating damping effect in GW. This also represents the most comprehensive tests on the modified GW propagations.

##### 8.Gravitational scattering upto third post-Newtonian approximation for conservative dynamics: Scalar-Tensor theories

**Authors:**Tamanna Jain

**Abstract:** We compute the scattering angle $\chi$ for hyperboliclike encounters in massless Scalar-Tensor (ST) theories up to third post-Newtonian (PN) order for the conservative part of the dynamics. To calculate the gauge-invariant scattering angle as a function of energy and orbital angular momentum, we use the approach of Effective-One-Body formalism as introduced in [Phys.Rev.D 96 (2017) 6, 064021]. We then compute the nonlocal-in-time contribution to the scattering angle by using the strategy of order-reduction of nonlocal dynamics introduced for small-eccentricity orbits.

##### 9.A practical guide to a moment approach for neutrino transport in numerical relativity

**Authors:**Carlo Musolino, Luciano Rezzolla

**Abstract:** The development of a neutrino moment based radiative-transfer code to simulate binary neutron-star mergers can easily become an obstacle path because of the numerous ways in which the solution of the equations may fail. We describe the implementation of the grey M1 scheme in our fully general-relativistic magnetohydrodynamics code and detail those choices and strategies that could lead either to a robust scheme or to a series of failures. In addition, we present new tests designed to show the consistency and accuracy of our code in conditions that are similar to realistic merging conditions and introduce a new, publicly available, benchmark based on the head-on collision of two neutron stars. This test, which is computationally less expensive than a complete merging binary but has all the potential pitfalls of the full scenario, can be used to compare future implementations of M1 schemes with the one presented here.

##### 1.Nonlinearly scalarized rotating black holes in Einstein-scalar-Gauss-Bonnet theory

**Authors:**Meng-Yun Lai, De-Cheng Zou, Rui-Hong Yue, Yun Soo Myung

**Abstract:** In this paper, we discuss a fully nonlinear mechanism for the formation of scalarized rotating black holes in EsGB gravity, where Kerr black holes are linearly stable, but unstable against nonlinear scalar perturbations. With the help of pseudo spectral method, we obtain the solutions of nonlinearly scalarized rotating black holes, and find a complicated spectrum of these black holes solutions with multiple scalarized branches. Moreover, we investigate the thermodynamic properties of nonlinearly scalarized rotating black holes and find the phase transition between Kerr and these black holes.

##### 2.Hybrid Proca-boson stars

**Authors:**Tian-Xiang Ma, Chen Liang, Jie Yang, Yong-Qiang Wang

**Abstract:** In this paper, we construct a hybrid boson star model that contains a complex scalar field and a Proca field. The scalar field is in the ground state, while the Proca field is in the first excited state. We numerically solve the model and obtain solution families of different coexisting states by considering both synchronized and nonsynchronized cases. By examining the relation between ADM mass and synchronized frequency $\tilde{\omega}$ or nonsynchronized frequency $\tilde{\omega}_P$, we identify several types of solution families for the hybrid boson stars. In addition to solutions that intersect the scalar field and the Proca field at each end, there are also several types of multi-branch coexisting state solutions. The characteristics of various solutions are analyzed and discussed in detail. We calculate the binding energy $E$ of the hybrid Proca-boson stars and provide the relationship between $E$ and both synchronized frequency $\tilde{\omega}$ and nonsynchronized frequency $\tilde{\omega}_P$. Furthermore, we obtain the stability of the corresponding hybrid star solution families from these analyses above.

##### 3.On the extended thermodynamics of the bumblebee black holes

**Authors:**Zhan-Feng Mai, Rui Xu, Dicong Liang, Lijing Shao

**Abstract:** As a vector-tensor theory including nonminimal coupling between the Ricci tensor and a vector field, the bumblebee gravity is a potential theory to test Lorentz symmetry violation. Recently, a new class of numerical spherical black holes in the bumblebee theory was constructed. In this paper, we investigate the associated local thermodynamic properties. By introducing a pair of conjugated thermodynamic quantities $X$ and $Y$, which can be interpreted as an extension of electric potential and charge of the Reissner Nordstr\"om black holes, we numerically construct a new first law of thermodynamics for bumblebee black holes. We then study the constant-$Y$ processes in the entropy-charge parameter space. For the constant-$Y$ processes, we also calculate the heat capacity to study the local thermodynamic stability of the bumblebee black holes. For a negative nonminimal coupling coefficient $\xi$, we find both divergent and smooth phase transitions. For a positive but small $\xi$, only a divergent phase transition is found. It turns out that there is a critical value $0.4\kappa <\xi_c < 0.5\kappa$ such that when $\xi_c < \xi<2\kappa$, even the divergent phase transition disappears and the bumblebee black holes thus become locally thermodynamically unstable regardless of the bumblebee charge. As for $\xi>2\kappa$, the smooth phase transition arises again but there no longer exists any discontinuous phase transition for the bumblebee black holes.

##### 4.Non-parametric inference of the population of compact binaries from gravitational wave observations using binned Gaussian processes

**Authors:**Anarya Ray, Ignacio Magaña Hernandez, Siddharth Mohite, Jolien Creighton, Shasvath Kapadia

**Abstract:** The observation of gravitational waves from multiple compact binary coalescences by the LIGO-Virgo-KAGRA detector networks has enabled us to infer the underlying distribution of compact binaries across a wide range of masses, spins, and redshifts. In light of the new features found in the mass spectrum of binary black holes and the uncertainty regarding binary formation models, non-parametric population inference has become increasingly popular. In this work, we develop a data-driven clustering framework that can identify features in the component mass distribution of compact binaries simultaneously with those in the corresponding redshift distribution, from gravitational wave data in the presence of significant measurement uncertainties, while making very few assumptions on the functional form of these distributions. Our generalized model is capable of inferring correlations among various population properties such as the redshift evolution of the shape of the mass distribution itself, in contrast to most existing non-parametric inference schemes. We test our model on simulated data and demonstrate the accuracy with which it can re-construct the underlying distributions of component masses and redshifts. We also re-analyze public LIGO-Virgo-KAGRA data from events in GWTC-3 using our model and compare our results with those from some alternative parametric and non-parametric population inference approaches. Finally, we investigate the potential presence of correlations between mass and redshift in the population of binary black holes in GWTC-3 (those observed by the LIGO-Virgo-KAGRA detector network in their first 3 observing runs), without making any assumptions about the specific nature of these correlations.

##### 5.Nonlinear instability and scalar clouds of spherical exotic compact objects in scalar-Gauss-Bonnet theory

**Authors:**Shao-Jun Zhang

**Abstract:** In this work, we present a new type of scalar clouds supported by spherically symmetric horizonless compact objects in the scalar-Gauss-Bonnet theory. Unlike the previous spontaneous scalarization that is triggered by the tachyonic instability, our scalarization arises from a nonlinear instability that is non-spontaneous. We explore two types of boundary conditions for the scalar field at the surface of the compact objects and find an infinite countable set of scalar clouds characterized by the number of nodes for both cases. Our study demonstrates that boundary conditions have a significant impact on the formation of scalar clouds. Specifically, for the Dirichlet boundary condition, scalarization is more likely to occur for compact objects with medium radii and becomes harder for ultra-compact and large ones. Conversely, for the Robin boundary condition, scalarization is easier for more compact objects.

##### 6.Strong Gravitational Lensing in Horndeski theory

**Authors:**Pedro Bessa

**Abstract:** In this paper we build the general formalism of gravitational lensing in luminal Horndeski theories, deriving the Jacobi matrix equation and the general angular diameter distance in these theories through the screen space formalism. We generalize the focusing and multiple lensing theorems to include Scalar Tensor theories belonging to the class and derive constraints they must satisfy to exhibit the same gravitional lensing behavior predicted by General Relativity. This provides a way to test theories through Strong Lensing effects, as well as a full theoretical framework for testing lensing in these theories. We find that for some subclasses, like metric $f(R)$ and unified $k$-essence, the conditions are satisified in general physical cases, while for others like Galileon Condensate models, the conditions impose constraints on the parameter space of the theory.

##### 7.Search for Postmerger Gravitational Waves from Binary Neutron Star Mergers Using a Matched-filtering Statistic

**Authors:**Andrzej Królak, Piotr Jaranowski, Michał Bejger, Paweł Ciecieląg, Orest Dorosh, Andrzej Pisarski

**Abstract:** In this paper, we present a new method to search for a short postmerger gravitational-wave signal following the merger of two neutron stars. Such a signal could follow the event GW170817 observed by LIGO and Virgo detectors. Our method is based on a matched filtering statistic and an approximate template of the postmerger signal in the form of a damped sinusoid. We test and validate our method using postmerger numerical simulations from the CoRe database. We find no evidence of the short postmerger signal in the LIGO data following the GW170817 event and we obtain upper limits. For short postmerger signals investigated, our best upper limit on the root sum square of the gravitational-wave strain emitted from 1.15 kHz to 4 kHz is $h_{\text{rss}}^{50\%}=1.8\times 10^{-22}/\sqrt{\text{Hz}}$ at 50% detection efficiency. The distance corresponding to this best upper limit is 4.64 Mpc.

##### 8.Fermi equation of state with finite temperature corrections in quantum space-times approach: Snyder model case

**Authors:**Anna Pachoł, Aneta Wojnar

**Abstract:** We investigate the impact of the deformed phase space associated with the quantum Snyder space on microphysical systems. The general Fermi-Dirac equation of state and specific corrections to it are derived. We put emphasis on non-relativistic degenerate Fermi gas as well as on the temperature-finite corrections to it. Considering the most general one-parameter family of deformed phase spaces associated with the Snyder model allows us to study whether the modifications arising in physical effects depend on the choice of realization. It turns out that we can distinguish three different cases with radically different physical consequences.

##### 9.Unifying inflation with early and late dark energy in Einstein-Gauss-Bonnet gravity

**Authors:**Shin'ichi Nojiri, Sergei D. Odintsov, Diego Sáez-Chillón Gómez

**Abstract:** In the era of precision cosmology, different observational data has led to precise measurements of the Hubble constant that differ significantly, what has been called the Hubble tension problem. In order to solve such a discrepancy, many different solutions have been proposed, from systematic errors on the observational data to theoretical proposals that assume an early dark energy that might affect the universe expansion at the time of recombination. In this paper, a model of varying cosmological constant is proposed in the framework of Einstein-Gauss-Bonnet gravity. The corresponding gravitational action is reconstructed and such a model is shown to reproduce well the inflationary era together with dark energy epoch and at the same time to provide an explanation for the discrepancy on the Hubble constant predictions. The transition to a phantom epoch is also realised, avoiding the usual instability problems of ordinary scalar field models.

##### 10.Controlled regularity at future null infinity from past asymptotic initial data: massless fields

**Authors:**Grigalius Taujanskas, Juan A. Valiente Kroon

**Abstract:** We study the relation between asymptotic characteristic initial data at past null infinity for the massless linear spin-s field equations and the regularity of the solutions at future null infinity. We quantitatively control the solutions to the spin-s equations on a causal rectangle reaching spatial infinity and containing portions of past and future null infinity. As a consequence, we show that even linear fields generically acquire polyhomogeneous expansions near future null infinity, with the regularity of the terms controlled precisely in terms of the regularity of the past characteristic initial data. Our analysis makes use of Friedrich's representation of spatial infinity together with a careful Gr\"onwall-type estimate that does not degenerate at the critical sets where null infinity meets spatial infinity, and Luk's strategy for the construction of optimal existence domains for the characteristic initial value problem.

##### 11.LISAmax: Improving the Gravitational-Wave Sensitivity by Two Orders of Magnitude

**Authors:**Waldemar Martens, Michael Khan, Jean-Baptiste Bayle

**Abstract:** Within its Voyage 2050 planning cycle, the European Space Agency (ESA) is considering long-term large class science mission themes. Gravitational-wave astronomy is among the topics under study. This paper presents "LISAmax", a gravitational-wave interferometer concept consisting of three spacecraft located close to the Sun-Earth libration points L3, L4 and L5, forming a triangular constellation with an arm length of 259 million kilometers (to be compared to LISA's 2.5 million kilometer arms). This is the largest triangular formation that can be reached from Earth without a major leap in mission complexity and cost. The sensitivity curve of such a detector is at least two orders of magnitude lower in amplitude than that of LISA. Depending on the choice of other instrument parameters, this makes the detector sensitive to gravitational waves in the micro-Hertz range and opens a new window for gravitational-wave astronomy, not covered by any other planned detector concept. We analyze in detail the constellation stability for a 10-year mission in the full numerical model and compute the orbit transfers using a European launcher and chemical propulsion. The payload design parameters are assessed, and the expected sensitivity curve is compared with a number of potential gravitational-wave sources. No show stoppers are identified at this point of the analysis.

##### 12.Exploring the multi-band gravitational wave background with a semi-analytic galaxy formation model

**Authors:**Zhencheng Li, Zhen Jiang, Xi-Long Fan, Yun Chen, Liang Gao, Shenghua Yu

**Abstract:** The compact binary systems, spanning from the stellar to supermassive black hole, encode a wealth of information concerning stellar evolution, galaxy formation and evolution, and cosmology. An enormous number of these systems, both resolved and unresolved, emit substantial gravitational waves during their final evolutionary stages, thereby creating a stochastic gravitational wave background (SGWB). We calculate the merger rates of stellar compact binaries and massive black hole binaries using a semi-analytic galaxy formation model -- Galaxy Assembly with Binary Evolution (GABE) in a unified and self-consistent approach, followed by an estimation of the multi-band SGWB contributed by the binary systems. We find that the amplitudes of the principal peaks of the SGWB energy density are within one order of magnitude $\Omega_{GW} \sim 10^{-9}- 10^{-8}$. This SGWB can be easily detected by the Square Kilometre Array (SKA), as well as planned interferometric detectors, such as the Einstein Telescope (ET) and the Laser Interferometer Space Antenna (LISA). The energy density of this background varies as $\Omega_{GW} \propto f^{2/3}$ in the SKA band. The shape of the SGWB spectrum in the frequency range $\sim[10^{-4}$,$1]$Hz could allow the space-based detector LISA to distinguish the black hole seed models. The amplitude of the SGWB from merging stellar binary black holes (BBHs) at $\sim 100$ Hz is approximately 10 and 100 times greater than those from merging binary neutron stars (BNSs) and neutron-star-black-hole (NSBH) mergers, respectively.

##### 13.Insight into the Microstructure of FRW Universe from a $P$-$v$ Phase Transition

**Authors:**Haximjan Abdusattar

**Abstract:** The $P$-$v$ phase transition of the FRW (Friedmann-Robertson-Walker) universe with a perfect fluid has recently been investigated, revealing that the four critical exponents near the critical point are consistent with the values predicted by mean field theory. Notably, the coexistence phase of the $P$-$v$ phase transition in the FRW universe above the critical temperature, which distinguishes it from van der Waals system and most of AdS black holes system. This unique property allows us to investigate the microstructure of the FRW universe as a thermodynamic system. Our analysis of the Ruppeiner thermodynamic geometry for the FRW universe reveals that the behavior of the scalar curvature near criticality is characterized by a dimensionless constant identical to that of the van der Waals fluid. Additionally, we observe that while repulsive interactions dominate for the coexistence large phase with higher temperature, the scalar curvature for the coexistence small phase is always negative, indicating attractive interactions, providing new insights into the nature of interactions among the perfect fluid matter constituents in the expanding FRW universe.

##### 14.Covariant spin-parity decomposition of the Torsion and Path Integrals

**Authors:**Riccardo Martini, Gregorio Paci, Dario Sauro

**Abstract:** We propose a functional measure over the torsion tensor. We discuss two completely equivalent choices for the Wheeler-DeWitt supermetric for this field, the first one being based on its algebraic decomposition, the other inspired by teleparallel theories of gravity. The measure is formally defined by requiring the normalization of the Gaussian integral. To achieve such a result we split the torsion tensor into its spin-parity eigenstates by constructing a new, York-like, decomposition. Of course, such a decomposition has a wider range of applicability to any kind of tensor sharing the symmetries of the torsion. As a result of this procedure a functional Jacobian naturally arises, whose formal expression is given exactly in the phenomenologically interesting limit of maximally symmetric spaces. We also discuss the explicit computation of this Jacobian in the case of a $4$-dimensional sphere $S^4$ with particular emphasis on its logarithmic divergences.

##### 15.Search for gravitational-lensing signatures in the full third observing run of the LIGO-Virgo network

**Authors:**The LIGO Scientific Collaboration, the Virgo Collaboration, the KAGRA Collaboration, R. Abbott, H. Abe, F. Acernese, K. Ackley, S. Adhicary, N. Adhikari, R. X. Adhikari, V. K. Adkins, V. B. Adya, C. Affeldt, D. Agarwal, M. Agathos, O. D. Aguiar, L. Aiello, A. Ain, P. Ajith, T. Akutsu, S. Albanesi, R. A. Alfaidi, C. Alléné, A. Allocca, P. A. Altin, A. Amato, S. Anand, A. Ananyeva, S. B. Anderson, W. G. Anderson, M. Ando, T. Andrade, N. Andres, M. Andrés-Carcasona, T. Andrić, S. Ansoldi, J. M. Antelis, S. Antier, T. Apostolatos, E. Z. Appavuravther, S. Appert, S. K. Apple, K. Arai, A. Araya, M. C. Araya, J. S. Areeda, M. Arène, N. Aritomi, N. Arnaud, M. Arogeti, S. M. Aronson, H. Asada, G. Ashton, Y. Aso, M. Assiduo, S. Assis de Souza Melo, S. M. Aston, P. Astone, F. Aubin, K. AultONeal, S. Babak, F. Badaracco, C. Badger, S. Bae, Y. Bae, S. Bagnasco, Y. Bai, J. G. Baier, J. Baird, R. Bajpai, T. Baka, M. Ball, G. Ballardin, S. W. Ballmer, G. Baltus, S. Banagiri, B. Banerjee, D. Bankar, J. C. Barayoga, B. C. Barish, D. Barker, P. Barneo, F. Barone, B. Barr, L. Barsotti, M. Barsuglia, D. Barta, J. Bartlett, M. A. Barton, I. Bartos, S. Basak, R. Bassiri, A. Basti, M. Bawaj, J. C. Bayley, M. Bazzan, B. Bécsy, V. M. Bedakihale, F. Beirnaert, M. Bejger, I. Belahcene, A. S. Bell, V. Benedetto, D. Beniwal, W. Benoit, J. D. Bentley, M. BenYaala, S. Bera, M. Berbel, F. Bergamin, B. K. Berger, S. Bernuzzi, M. Beroiz, C. P. L. Berry, D. Bersanetti, A. Bertolini, J. Betzwieser, D. Beveridge, R. Bhandare, A. V. Bhandari, U. Bhardwaj, R. Bhatt, D. Bhattacharjee, S. Bhaumik, A. Bianchi, I. A. Bilenko, M. Bilicki, G. Billingsley, S. Bini, O. Birnholtz, S. Biscans, M. Bischi, S. Biscoveanu, A. Bisht, B. Biswas, M. Bitossi, M. -A. Bizouard, J. K. Blackburn, C. D. Blair, D. G. Blair, R. M. Blair, F. Bobba, N. Bode, M. Boër, G. Bogaert, M. Boldrini, G. N. Bolingbroke, L. D. Bonavena, R. Bondarescu, F. Bondu, E. Bonilla, R. Bonnand, P. Booker, R. Bork, V. Boschi, N. Bose, S. Bose, V. Bossilkov, V. Boudart, Y. Bouffanais, A. Bozzi, C. Bradaschia, P. R. Brady, A. Bramley, A. Branch, M. Branchesi, J. E. Brau, M. Breschi, T. Briant, J. H. Briggs, A. Brillet, M. Brinkmann, P. Brockill, A. F. Brooks, J. Brooks, D. D. Brown, S. Brunett, G. Bruno, R. Bruntz, J. Bryant, F. Bucci, J. Buchanan, T. Bulik, H. J. Bulten, A. Buonanno, K. Burtnyk, R. Buscicchio, D. Buskulic, C. Buy, R. L. Byer, G. S. Cabourn Davies, G. Cabras, R. Cabrita, L. Cadonati, G. Cagnoli, C. Cahillane, J. Calderón Bustillo, J. D. Callaghan, T. A. Callister, E. Calloni, J. B. Camp, M. Canepa, G. Caneva, M. Cannavacciuolo, K. C. Cannon, H. Cao, Z. Cao, L. A. Capistran, E. Capocasa, E. Capote, G. Carapella, F. Carbognani, M. Carlassara, J. B. Carlin, M. Carpinelli, G. Carrillo, J. J. Carter, G. Carullo, J. Casanueva Diaz, C. Casentini, G. Castaldi, S. Caudill, M. Cavaglià, F. Cavalier, R. Cavalieri, G. Cella, P. Cerdá-Durán, E. Cesarini, W. Chaibi, W. Chakalis, S. Chalathadka Subrahmanya, E. Champion, C. -H. Chan, C. Chan, C. L. Chan, K. Chan, M. Chan, K. Chandra, I. P. Chang, W. Chang, P. Chanial, S. Chao, C. Chapman-Bird, P. Charlton, E. Chassande-Mottin, C. Chatterjee, Debarati Chatterjee, Deep Chatterjee, M. Chaturvedi, S. Chaty, K. Chatziioannou, C. Chen, D. Chen, H. Y. Chen, J. Chen, K. Chen, X. Chen, Y. -B. Chen, Y. -R. Chen, Y. Chen, H. Cheng, P. Chessa, H. Y. Cheung, H. Y. Chia, F. Chiadini, C-Y. Chiang, G. Chiarini, R. Chierici, A. Chincarini, M. L. Chiofalo, A. Chiummo, R. K. Choudhary, S. Choudhary, N. Christensen, Q. Chu, Y-K. Chu, S. S. Y. Chua, K. W. Chung, G. Ciani, P. Ciecielag, M. Cieślar, M. Cifaldi, A. A. Ciobanu, R. Ciolfi, F. Clara, J. A. Clark, T. A. Clarke, P. Clearwater, S. Clesse, F. Cleva, E. Coccia, E. Codazzo, P. -F. Cohadon, D. E. Cohen, M. Colleoni, C. G. Collette, A. Colombo, M. Colpi, C. M. Compton, L. Conti, S. J. Cooper, P. Corban, T. R. Corbitt, I. Cordero-Carrión, S. Corezzi, N. J. Cornish, A. Corsi, S. Cortese, A. C. Coschizza, R. Cotesta, R. Cottingham, M. W. Coughlin, J. -P. Coulon, S. T. Countryman, B. Cousins, P. Couvares, D. M. Coward, M. J. Cowart, D. C. Coyne, R. Coyne, K. Craig, J. D. E. Creighton, T. D. Creighton, A. W. Criswell, M. Croquette, S. G. Crowder, J. R. Cudell, T. J. Cullen, A. Cumming, R. Cummings, E. Cuoco, M. Curyło, P. Dabadie, T. Dal Canton, S. Dall'Osso, G. Dálya, A. Dana, B. D'Angelo, S. Danilishin, S. D'Antonio, K. Danzmann, C. Darsow-Fromm, A. Dasgupta, L. E. H. Datrier, Sayak Datta, Sayantani Datta, V. Dattilo, I. Dave, M. Davier, D. Davis, M. C. Davis, E. J. Daw, M. Dax, D. DeBra, M. Deenadayalan, J. Degallaix, M. De Laurentis, S. Deléglise, V. Del Favero, F. De Lillo, N. De Lillo, D. Dell'Aquila, W. Del Pozzo, F. De Matteis, V. D'Emilio, N. Demos, T. Dent, A. Depasse, R. De Pietri, R. De Rosa, C. De Rossi, R. DeSalvo, R. De Simone, S. Dhurandhar, R. Diab, M. C. Díaz, N. A. Didio, T. Dietrich, L. Di Fiore, C. Di Fronzo, C. Di Giorgio, F. Di Giovanni, M. Di Giovanni, T. Di Girolamo, D. Diksha, A. Di Lieto, A. Di Michele, S. Di Pace, I. Di Palma, F. Di Renzo, A. K. Divakarla, A. Dmitriev, Z. Doctor, P. P. Doleva, L. Donahue, L. D'Onofrio, F. Donovan, K. L. Dooley, T. Dooney, S. Doravari, O. Dorosh, M. Drago, J. C. Driggers, Y. Drori, J. -G. Ducoin, L. Dunn, U. Dupletsa, O. Durante, D. D'Urso, P. -A. Duverne, S. E. Dwyer, C. Eassa, P. J. Easter, M. Ebersold, T. Eckhardt, G. Eddolls, B. Edelman, T. B. Edo, O. Edy, A. Effler, S. Eguchi, J. Eichholz, S. S. Eikenberry, M. Eisenmann, R. A. Eisenstein, A. Ejlli, E. Engelby, Y. Enomoto, L. Errico, R. C. Essick, H. Estellés, D. Estevez, T. Etzel, M. Evans, T. M. Evans, T. Evstafyeva, B. E. Ewing, J. M. Ezquiaga, F. Fabrizi, F. Faedi, V. Fafone, H. Fair, S. Fairhurst, P. C. Fan, A. M. Farah, B. Farr, W. M. Farr, G. Favaro, M. Favata, M. Fays, M. Fazio, J. Feicht, M. M. Fejer, E. Fenyvesi, D. L. Ferguson, A. Fernandez-Galiana, I. Ferrante, T. A. Ferreira, F. Fidecaro, P. Figura, A. Fiori, I. Fiori, M. Fishbach, R. P. Fisher, R. Fittipaldi, V. Fiumara, R. Flaminio, E. Floden, H. K. Fong, J. A. Font, B. Fornal, P. W. F. Forsyth, A. Franke, S. Frasca, F. Frasconi, J. P. Freed, Z. Frei, A. Freise, O. Freitas, R. Frey, P. Fritschel, V. V. Frolov, G. G. Fronzé, Y. Fujii, Y. Fujikawa, Y. Fujimoto, P. Fulda, M. Fyffe, H. A. Gabbard, W. E. Gabella, B. U. Gadre, J. R. Gair, J. Gais, S. Galaudage, R. Gamba, D. Ganapathy, A. Ganguly, D. -F. Gao, D. Gao, S. G. Gaonkar, B. Garaventa, C. García-Núñez, C. García-Quirós, K. A. Gardner, J. Gargiulo, F. Garufi, C. Gasbarra, B. Gateley, V. Gayathri, G. -G. Ge, G. Gemme, A. Gennai, J. George, O. Gerberding, L. Gergely, S. Ghonge, Abhirup Ghosh, Archisman Ghosh, Shaon Ghosh, Shrobana Ghosh, Tathagata Ghosh, L. Giacoppo, J. A. Giaime, K. D. Giardina, D. R. Gibson, C. Gier, P. Giri, F. Gissi, S. Gkaitatzis, J. Glanzer, A. E. Gleckl, F. G. Godoy, P. Godwin, E. Goetz, R. Goetz, J. Golomb, B. Goncharov, G. González, M. Gosselin, R. Gouaty, D. W. Gould, S. Goyal, B. Grace, A. Grado, V. Graham, M. Granata, V. Granata, S. Gras, P. Grassia, C. Gray, R. Gray, G. Greco, A. C. Green, R. Green, A. M. Gretarsson, E. M. Gretarsson, D. Griffith, W. L. Griffiths, H. L. Griggs, G. Grignani, A. Grimaldi, S. J. Grimm, H. Grote, S. Grunewald, A. S. Gruson, D. Guerra, G. M. Guidi, A. R. Guimaraes, H. K. Gulati, F. Gulminelli, A. M. Gunny, H. -K. Guo, Y. Guo, Anchal Gupta, Anuradha Gupta, P. Gupta, S. K. Gupta, J. Gurs, R. Gustafson, N. Gutierrez, F. Guzman, S. Ha, I. P. W. Hadiputrawan, L. Haegel, S. Haino, O. Halim, E. D. Hall, E. Z. Hamilton, G. Hammond, W. -B. Han, M. Haney, J. Hanks, C. Hanna, M. D. Hannam, O. Hannuksela, H. Hansen, J. Hanson, R. Harada, T. Harder, K. Haris, J. Harms, G. M. Harry, I. W. Harry, D. Hartwig, K. Hasegawa, B. Haskell, C. -J. Haster, J. S. Hathaway, K. Hattori, K. Haughian, H. Hayakawa, K. Hayama, F. J. Hayes, J. Healy, A. Heidmann, A. Heidt, M. C. Heintze, J. Heinze, J. Heinzel, H. Heitmann, F. Hellman, P. Hello, A. F. Helmling-Cornell, G. Hemming, M. Hendry, I. S. Heng, E. Hennes, J. -S. Hennig, M. Hennig, C. Henshaw, A. G. Hernandez, F. Hernandez Vivanco, M. Heurs, A. L. Hewitt, S. Higginbotham, S. Hild, P. Hill, Y. Himemoto, A. S. Hines, N. Hirata, C. Hirose, T-C. Ho, S. Hochheim, D. Hofman, J. N. Hohmann, D. G. Holcomb, N. A. Holland, I. J. Hollows, Z. J. Holmes, K. Holt, D. E. Holz, Q. Hong, J. Hough, S. Hourihane, D. Howell, E. J. Howell, C. G. Hoy, D. Hoyland, A. Hreibi, B-H. Hsieh, H-F. Hsieh, C. Hsiung, H-Y. Huang, P. Huang, Y-C. Huang, Y. -J. Huang, Y. Huang, M. T. Hübner, A. D. Huddart, B. Hughey, D. C. Y. Hui, V. Hui, S. Husa, S. H. Huttner, R. Huxford, T. Huynh-Dinh, J. Hyland, G. A. Iandolo, S. Ide, B. Idzkowski, A. Iess, K. Inayoshi, Y. Inoue, P. Iosif, J. Irwin, Ish Gupta, M. Isi, K. Ito, Y. Itoh, B. R. Iyer, V. JaberianHamedan, T. Jacqmin, P. -E. Jacquet, S. J. Jadhav, S. P. Jadhav, T. Jain, A. L. James, A. Z. Jan, K. Jani, J. Janquart, K. 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**Abstract:** Gravitational lensing by massive objects along the line of sight to the source causes distortions of gravitational wave-signals; such distortions may reveal information about fundamental physics, cosmology and astrophysics. In this work, we have extended the search for lensing signatures to all binary black hole events from the third observing run of the LIGO--Virgo network. We search for repeated signals from strong lensing by 1) performing targeted searches for subthreshold signals, 2) calculating the degree of overlap amongst the intrinsic parameters and sky location of pairs of signals, 3) comparing the similarities of the spectrograms amongst pairs of signals, and 4) performing dual-signal Bayesian analysis that takes into account selection effects and astrophysical knowledge. We also search for distortions to the gravitational waveform caused by 1) frequency-independent phase shifts in strongly lensed images, and 2) frequency-dependent modulation of the amplitude and phase due to point masses. None of these searches yields significant evidence for lensing. Finally, we use the non-detection of gravitational-wave lensing to constrain the lensing rate based on the latest merger-rate estimates and the fraction of dark matter composed of compact objects.

##### 16.Event horizon gluing and black hole formation in vacuum: the very slowly rotating case

**Authors:**Christoph Kehle, Ryan Unger

**Abstract:** In this paper, we initiate the study of characteristic event horizon gluing in vacuum. More precisely, we prove that Minkowski space can be glued along a null hypersurface to any round symmetry sphere in a Schwarzschild black hole spacetime as a $C^2$ solution of the Einstein vacuum equations. The method of proof is fundamentally nonperturbative and is closely related to our previous work in spherical symmetry [KU22] and Christodoulou's short pulse method [Chr09]. We also make essential use of the perturbative characteristic gluing results of Aretakis-Czimek-Rodnianski [ACR21a; CR22]. As an immediate corollary of our methods, we obtain characteristic gluing of Minkowski space to the event horizon of very slowly rotating Kerr with prescribed mass $M$ and specific angular momentum $a$. Using our characteristic gluing results, we construct examples of vacuum gravitational collapse to very slowly rotating Kerr black holes in finite advanced time with prescribed $M$ and $0\le |a|\ll M$. Our construction also yields the first example of a spacelike singularity arising from one-ended, asymptotically flat gravitational collapse in vacuum.

##### 17.A stationary axisymmetric vacuum solution for pure $R^2$ gravity

**Authors:**Mustapha Azreg-Aïnou, Hoang Ky Nguyen

**Abstract:** The closed-form expression for pure $R^2$ vacuum solution obtained in arXiv:2211.03542 [gr-qc] (to appear in Phys. Rev. D) lends itself to a generalization to axisymmetric setup via the modified Newman-Janis algorithm. We adopt the procedure put forth in Phys. Rev. D 90, 064041 (2014) bypassing the complexification of the radial coordinate. The procedure presumes the existence of Boyer-Lindquist coordinates. Using the Event Horizon Telescope Collaboration results, we model the central black hole M87* by the thus obtained exact rotating metric, depending on the mass, rotation parameter and a third dimensionless parameter. The latter is constrained upon investigating the shadow angular size assuming mass and rotation parameters are those of M87*.

##### 1.Hunting the stochastic gravitational wave background in pulsar timing array cross correlations through theoretical uncertainty

**Authors:**Reginald Christian Bernardo, Kin-Wang Ng

**Abstract:** Incredible progress on the theoretical uncertainty of the spatial correlations of the stochastic gravitational wave (GW) background were recently made. However, it remains to realize the impact of this theoretical uncertainty on PTA cross correlations analysis. This paper pushes forward in this direction, as a proof--of--principle: showing the potential role that theoretical uncertainty has on unburying the stochastic GW background signal in noisy PTA cross correlation measurements. We consider both a mock data set and the noise--marginalized 12.5 years NANOGrav spatial correlation measurements, and find optimistic conclusions regardless of the physical content of the GW background and the nature of the noise in the data. Very briefly, we show through various cases a modest, but profound result that looking out for a stochastic signal is better when two of its moments are utilized. Or, in terms of GWs, we show that the theoretical uncertainty can play a substantial role in the hunt for the stochastic GW background.

##### 2.Axionic extension of the Einstein-Dirac-aether theory: Degeneracy removal with respect to shear of the aether flow

**Authors:**Anna O. Efremova, Alexander B. Balakin

**Abstract:** We consider dynamics of the quartet of interacting cosmic substrata, which includes the dynamic aether, presented by the unit timelike vector field, the axionic dark matter, described by the pseudoscalar field, the spinor field associated with fermion particles, and the gravity field. The extended set of master equations is derived based on the idea that the potential of the axion field to be the function of seven arguments. The first one is, standardly, the pseudoscalar field; the second and third arguments are the fundamental spinor invariant and pseudoinvariant; the fourth and fifth ones are the aether-axion cross-invariants and cross-pseudoinvariants; the sixth argument is the expansion scalar, and the seventh one is the square of tensor of the shear of the aether flow. The complete set of master equations is derived and prepared for analysis.

##### 3.Nonlinear interaction of the axion field with dynamic aether and SU(2) symmetric gauge field in the anisotropic Universe

**Authors:**Alexander B. Balakin, Gleb B. Kiselev

**Abstract:** Based on the concept of the dynamic aether emergence as a result of spontaneous polarization of the color aether, we consider the SU(2) symmetric theory of interaction of the gauge and axion fields in the framework of anisotropic cosmological model of the Bianchi-I type. We focus on the analysis of the non-Abelian analog of the U(1) symmetric model of axionically induced generation of the electric field in a magnetized medium.

##### 4.Axion electrodynamics on the Bianchi spacetime platform: Fingerprints of shear of the aether velocity

**Authors:**Amir F. Shakirzyanov, Alexander B. Balakin

**Abstract:** In the framework of axionically extended Einstein-Maxwell-aether theory we study the structure of the electromagnetic field allowed by the anisotropic cosmological spacetime platforms associated with the Bianchi models. These models guarantee that the aether velocity possesses the shear, and we focus on its role in the evolution of the axion-photon systems. In this short note we discuss the extended master equations obtained under the assumption that the square of the shear tensor is included in the potential of the axion field.

##### 5.Nonlocal extension of relativistic non-equilibrium thermostatics

**Authors:**Alexei S. Ilin, Alexander B. Balakin

**Abstract:** Based on the formalism of nonlocal extension of the Israel-Stewart causal thermodynamics on the one hand, and on the formalism of the extended thermostatics on the other hand, we propose the new model of nonlocal relativistic non-equilibrium thermostatics for description of the static spherically symmetric stellar systems. This nonlocal formalism operates with the pair of orthogonal four-vectors: one of them is the standard unit timelike medium velocity four-vector, the second one is the unit spacelike director. We derived the extended equation describing the profile of the non-equilibrium pressure, which can be indicated as the static analog of the Burgers constitutive equation known in classical rheology.

##### 6.Parity violating scalar-tensor model in teleparallel gravity and its cosmological application

**Authors:**Haomin Rao, Dehao Zhao

**Abstract:** The parity violating model based on teleparallel gravity is a competitive scheme for parity violating gravity, which has been preliminary studied in the literature. To further investigate the parity violating model in teleparallel gravity, in this paper, we construct all independent parity-odd terms that are quadratic in torsion tensor and coupled to a scalar field in a way without higher-order derivatives. Using these parity-odd terms, we formulate a general parity violating scalar-tensor model in teleparallel gravity and obtain its equations of motion. To explore potentially viable models within the general model, we investigate the cosmological application of a submodel of the general model in which terms above the second power of torsion are eliminated. We focus on analyzing cosmological perturbations and identify the conditions that preserve the parity violating signal of gravitational waves at linear order while avoiding the ghost instability.

##### 7.Ricci Inverse Anisotropic Stellar Structures

**Authors:**M. Farasat Shamir, Mushtaq Ahmad, G. Mustafa, Aisha Rashid

**Abstract:** This paper offers novel quintessence compact relativistic spherically symmetrical anisotropic solutions under the recently developed Ricci inverse gravity Amendola et al., 2020), by employing Krori and Barua gravitational potentials, $Ar^2=\nu(r), ~\&~Br^2+C=\mu(r)$ (with A, B, and C being real constants). For this objective, a specific explicit equation of state, connecting energy density and radial pressure, i.e., $p_r=\omega\rho$, such that $0<\omega<1$, has been utilized with an anisotripic fluid source. Ricci inverse field equations are used to find the exclusive expressions of the energy density, radial and tangential stresses, and the quintessence energy density, the critical physical attributes reflecting the exceptional conduct of extremely dense matter configuration. For the observatory source stars $Her X-1$, $SAX J 1808.4-3658$ and $4U 1820-30$, all the important physical quantities like energy densities, tangential and radial pressures, energy conditions, gradients, anisotropy, redshift and mass-radius functions, and stellar compactness have been worked out and analyzed graphically. It has been concluded that all of the stellar formations under consideration remain free from any undesirable central singularity and are stable.

##### 8.Probing extra dimensions through cosmological observations of dark energy

**Authors:**R. Jalalzadeh, S. Jalalzadeh, B. Malekolkalami

**Abstract:** We investigate the isometrically embedded Bianchi type-V cosmology braneworld model in a $D$-dimensional bulk space. The model provides a fluid of geometric dark energy (GDE) and unification of fundamental forces similar to the Kaluza--Klein (KK) theory. The Planck energy density, the fine structure constant, the muon mass, and the number of extra dimensions are all factors that determine the density of the induced GDE. The model also predicts that graviton has mass, which is determined by the induced cosmological constant (CC). Our results are compatible with observations of the standard model of cosmology if the Universe has 22 non-compact extra dimensions. Our model provides an alternative method for probing extra dimensions.

##### 1.Existence of Wormholes in $f(\mathcal{G})$ Gravity using Symmetries

**Authors:**Tayyaba Naz, G. Mustafa, M. Farasat Shamir

**Abstract:** The current study examines the geometry of static wormholes with anisotropic matter distribution in context of modified $f(\mathcal{G})$ gravity. We consider the well known Noether and conformal symmetries, which help in investigating wormholes in $f(\mathcal{G})$ gravity. For this purpose, we develop symmetry generators associated with conserved quantities by taking into consideration the $f(\mathcal{G})$ gravity model. Moreover, we use the conservation relationship gained from the classical Noether method and conformal Killing symmetries to develop the metric potential. These symmetries provide a strong mathematical background to investigate wormhole solutions by incorporating some suitable initial conditions. The obtained conserved quantity performs a significant role in defining the essential physical characteristics of the shape-function and energy conditions. Further, we also describe the stability of obtained wormholes solutions by employing the equilibrium condition in modified $f(\mathcal{G})$ gravity. It is observed from graphical representation of obtained wormhole solutions that Noether and conformal Killing symmetries provide the results with physically accepted patterns.

##### 2.Fine tuning of rainbow gravity functions and Klein-Gordon particles in cosmic string rainbow gravity spacetime

**Authors:**Omar Mustafa

**Abstract:** We argue that, as long as relativistic quantum particles are in point, the variable $y=E/E_p$ of the rainbow functions pair $g_{_{0}} (y)$ and $g_{_{1}} (y)$ should be fine tuned into $y=|E|/E_p$, where $E_p$ is the Planck's energy scale. Otherwise, the rainbow functions will be only successful to describe the rainbow gravity effect on relativistic quantum particles and the anti-particles will be left unfortunate. Under such fine tuning, we consider Klein-Gordon (KG) particles in cosmic string rainbow gravity spacetime in a non-uniform magnetic field (i.e., $\mathbf{B}=\mathbf{\nabla }\times \mathbf{A}=\frac{3}{2}B_{\circ }r\,\hat{z}$ ). Then we consider KG-particles in cosmic string rainbow gravity spacetime in a uniform magnetic field (i.e., $\mathbf{B}=\mathbf{\nabla }\times \mathbf{A}=\frac{1}{2}B_{\circ }\,\hat{z}$ ). Whilst the former effectively yields KG-oscillators, the later effectively yields KG-Coulombic particles. We report on the effects of rainbow gravity on both KG-oscillators and Coulombic particles using four pairs of rainbow functions: (i) $% g_{_{0}}\left( y\right) =1$, $g_{_{1}}\left( y\right) =\sqrt{1-\epsilon y^{2}% }$, (ii) $g_{_{0}}\left( y\right) =1$, $g_{_{1}}\left( y\right) =\sqrt{% 1-\epsilon y}$, (iii) $g_{_{0}}\left( y\right) =g_{_{1}}\left( y\right) =\left( 1-\epsilon y\right) ^{-1}$, and (iv) $g_{_{0}}\left( y\right) =\left( e^{\epsilon y}-1\right) /\epsilon y$, $g_{_{1}}\left( y\right) =1$, where $y=|E|/E_p$ and $\epsilon$ is the rainbow parameter. It is interesting to report that, all KG particles' and anti-particles' energies are symmetric about $E=0$ value (a natural relativistic quantum mechanical tendency), and a phenomenon of energy states to fly away and disappear from the spectrum is observed for the rainbow functions pair (iii) at $\gamma=\epsilon m/E_p=1$.

##### 3.Entanglement entropy for spherically symmetric regular black holes

**Authors:**Orlando Luongo, Stefano Mancini, Paolo Pierosara

**Abstract:** The Bardeen and Hayward spacetimes are here considered as standard configurations of spherically symmetric regular black holes. Assuming the thermodynamics of such objects to be analogous to standard black holes, we compute the island formula in the regime of small topological charge and vacuum energy, respectively for Bardeen and Hayward spacetimes. Late and early-time domains are separately discussed, with particular emphasis on the island formations. We single out conditions under which it is not possible to find out islands at early-times and how our findings depart from the standard Schwarzschild case. Motivated by th fact that those configurations extend Reissner-Nordstr\"{o}m and Schwarzschild-de Sitter metrics through the inclusion of regularity behavior at $r=0$, we show how the effects of regularity induces modifications on the overall entanglement entropy. Finally, the Page time is also computed and we thus show which asymptotic values are expected for it, for all the configurations under exam. The Page time shows slight departures than the Schwarzschild case, especially for the Hayward case, while the Bardeen regular black hole turns out to be quite indistinguishable from the Schwarzschild case.

##### 4.Chaotic interactions between dark matter and dark energy

**Authors:**E. Aydiner

**Abstract:** In this study, we consider dark matter and dark energy as grand-canonical systems which are open, non-equilibrium coupled, and interacting systems. It is the first time, we propose a new more realistic interaction schema to explain dynamics between coupled interacting thermodynamic systems. Based on this new interaction schema, we propose new theorems to define the interactions. We proved the theorems based on the energy conservation law of thermodynamics. Furthermore, we obtain new coupled equations using the theorems. We numerically solve the interaction equations and obtained phase space diagrams and Lyapunov exponents. We show that the interaction between dark matter and dark energy is chaotic. We conclude that these theorems and results can be generalized to all coupled interacting non-equilibrium systems. Finally, we give a new definition of chaos.

##### 5.Prospects for detecting anisotropies and polarization of the stochastic gravitational wave background with ground-based detectors

**Authors:**Giorgio Mentasti, Carlo Contaldi, Marco Peloso

**Abstract:** We build an analytical framework to study the observability of anisotropies and a net chiral polarization of the Stochastic Gravitational Wave Background (SGWB) with a generic network of ground-based detectors. We apply this formalism to perform a Fisher forecast of the performance of a network consisting of the current interferometers (LIGO, Virgo and KAGRA) and planned third-generation ones, such as the Einstein Telescope and Cosmic Explorer. Our results yield limits on the observability of anisotropic modes, spanning across noise- and signal-dominated regimes. We find that if the isotropic component of the SGWB has an amplitude close to the current limit, third-generation interferometers with an observation time of $10$ years can measure multipoles (in a spherical harmonic expansion) up to $\ell = 8$ with ${\cal O }\left( 10^{-3} - 10^{-2} \right)$ accuracy relative to the isotropic component, and an ${\cal O }\left( 10^{-3} \right)$ amount of net polarization. For weaker signals, the accuracy worsens as roughly the inverse of the SGWB amplitude.

##### 6.$f(\mathcal{G},\mathrm{\textit{T}})$ Gravity Bouncing Universe with Cosmological Parameters

**Authors:**Mushtaq Ahmad, M. Farasat Shamir, G. Mustafa

**Abstract:** In recent few years, the Gauss-Bonnet $f(\mathcal{G},\mathrm{\textit{T}})$ theory of gravity has fascinated considerable researchers owing to its coupling of trace of the stress-energy tensor $T$ with the Gauss-Bonnet term $\mathcal{G}$. In this context, we focuss ourselves to study bouncing universe with in $f(\mathcal{G},\mathrm{\textit{T}})$ gravity background. Some important preliminaries are presented along with the discussion of cosmological parameters to develop a minimal background about $f(\mathcal{G},\mathrm{\textit{T}})$ theory of gravity. The exact bouncing solutions with physical analysis are provided with the choice of two equation of state parameters. It is shown that the results do agree with the present values of deceleration, jerk and snap parameters. Moreover, it is concluded that the model parameters are quite important for the validity of conservation equation (as the matter coupled theories do not obey the usual conservation law).

##### 1.Surface Gravity of Dynamical Horizons: A Causal Perspective

**Authors:**Anamika Avinash Pathak, Konka Raviteja, Swastik Bhattacharya, Sashideep Gutti

**Abstract:** We consider marginally trapped surfaces in a spherically symmetric spacetime evolving due to the presence of a perfect fluid in D-dimensions and look at the various definitions of the surface gravity for these marginally trapped surfaces. We show that using Einstein equations it is possible to simplify and obtain general formulae for the surface gravity in terms of invariant quantities defined at these marginally trapped surfaces like area radius, cosmological constant and principal values of the energy-momentum tensor \r{ho}, p. We then correlate these expressions of surface gravity to the cases of dynamical horizons and timelike tubes and find which proposals of surface gravity are causally sensitive as these surfaces undergo causal transitions from spacelike to timelike and vice versa.

##### 2.Relativistic Krori-Barua Compact Stars in $f(R,T)$ Gravity

**Authors:**M. Farasat Shamir, Zoya Asghar, Adnan Malik

**Abstract:** This work aims to investigate the behaviour of compact stars in the background of $f(R, T)$ theory of gravity. For current work, we consider the Krori-Barua metric potential i.e., $\nu(r)= Br^2+C$ and $\lambda(r)= Ar^2,$ where, $A, B$ and $C$ are constants. We use matching conditions of spherically symmetric space-time with Schwarzschild solution as an exterior geometry and examine the physical behaviour of stellar structure by assuming the exponential type $f(R, T)$ gravity model. In the present analysis, we discuss the graphical behaviour of energy density, radial pressure, tangential pressure, equation of state parameters, anisotropy and stability analysis respectively. Furthermore, an equilibrium condition can be visualized through the modified Tolman-Oppenheimer-Volkov equation. Some extra features of compact stars i.e. mass-radius function, compactness factor and surface redshift have also been investigated. Conclusively, all the results in current study validate the existence of compact stars under exponential $f(R, T)$ gravity model.

##### 3.Asymptotic solution of inflationary T-models in the Hamilton-Jacobi formalism

**Authors:**Gabriel Álvarez, Elena Medina

**Abstract:** We use the Hamilton-Jacobi formalism to derive asymptotic solutions to the dynamical equations for inflationary T-models in a flat Friedmann-Lema\^itre-Robertson-Walker spacetime in the kinetic dominance stage and in the slow-roll stage. With an appropriate Pad\'e summation, the expansions for the Hubble parameter can be matched, which in turn determines the relation between the expansions for the scale factor and allows us to compute the total amount of inflation as a function of the initial data or, conversely, to select initial data that correspond to a fixed total amount of inflation. Other magnitudes of interest, like the first slow roll parameter (and consequently the equation of state parameter) can be described in parametric form using the inflation field itself as a parameter.

##### 4.Accretion process of a black hole in scalar field dark energy model

**Authors:**M. Koussour

**Abstract:** We propose a logarithmic parametrization form of energy density for the scalar field dark energy in the framework of the standard theory of gravity, which supports the necessary transition from the decelerated to the accelerated periods of the Universe. The analyzed model has a parameter space that is constrained by available observational data, including cosmic chronometers data-sets (CC), Baryonic Acoustic Oscillation (BAO) data-sets, and Supernovae (SN) data-sets, consisting of only two parameters $\alpha$ and $\beta$. The combined $CC$+$BAO$+$SN$ data-sets yields a transition redshift of $z_{tr}=0.79^{+0.02}_{-0.02}$, where the model exhibits signature-flipping and is consistent with recent observations. For the combined data-sets, the present value of the deceleration parameter is calculated to be $q_{0}=-0.43^{+0.06}_{-0.06}$. Furthermore, the analysis yields constraints on both the parameter density value for matter and the present value of the Hubble parameter, with values of $\Omega_{m0}=0.25849^{+0.00026}_{-0.00025}$ and $H_{0}=67.79_{-0.59}^{+0.59}km/s/Mpc$, respectively, consistent with the results obtained from Planck 2018. Finally, the study investigates how the mass of a black hole evolves over time in a Universe with both matter and dark energy. It reveals that the black hole mass increases initially but stops increasing as dark energy dominates.

##### 5.Geodesic completeness of effective null geodesics in regular space-times with non-linear electrodynamics

**Authors:**Merce Guerrero, Gonzalo J. Olmo, Diego Rubiera-Garcia

**Abstract:** We study the completeness of light trajectories in certain spherically symmetric regular geometries found in Palatini theories of gravity threaded by non-linear (electromagnetic) fields, which makes their propagation to happen along geodesics of an effective metric. Two types of geodesic restoration mechanisms are employed: by pushing the focal point to infinite affine distance, thus unreachable in finite time by any sets of geodesics, or by the presence of a defocusing surface associated to the development of a wormhole throat. We discuss several examples of such geometries to conclude the completeness of all such effective paths. Our results are of interest both for the finding of singularity-free solutions and for the analysis of their optical appearances e.g. in shadow observations.

##### 6.Complexity and simplicity of self-gravitating fluids

**Authors:**L. Herrera

**Abstract:** We review a recently proposed definition of complexity of the structure of self--gravitating fluids \cite{ch1}, and the criterium to define the simplest mode of their evolution. We analyze the origin of these concepts and their possible applications in the study of gravitation collapse. We start by considering the static spherically symmetric case, extending next the study to static axially symmetric case. Afterward we consider the non--static spherically symmetric case. Two possible modes of evolution are proposed to be the simplest one. One is the homologous conditio,, however, as was shown later on, it may be useful to relax this last condition to enlarge the set of possible solutions, by adopting the so-called quasi-homologous condition. As another example of symmetry, we consider fluids endowed with hyperbolical symmetry. Exact solutions for static fluid distributions satisfying the condition of minimal complexity are presented.. An extension of the complexity factor to the vacuum solutions of the Einstein equations represented by the Bondi metric is discussed. A complexity hierarchy is established in this case, ranging from the Minkowski spacetime (the simplest one) to gravitationally radiating systems (the most complex). Finally we propose a list of questions which, we believe, deserve to be treated in the future

##### 7.Reheating constraints in Instant Preheating

**Authors:**Jaume de Haro

**Abstract:** We use Instant Preheating as a mechanism to reheat the universe when its evolution is modeled by a non-oscillating background. Once we obtain the reheating temperature, we calculate the number of e-folds using two different methods, which allows us to establish a relationship between the reheating temperature and the spectral index of scalar perturbations. We explore this connection to constrain the spectral index for different Quintessential Inflation models.

##### 1.Defrosting frozen stars: spectrum of internal fluid modes

**Authors:**Ram Brustein, A. J. M. Medved, Tom Shindelman

**Abstract:** The frozen star model provides a classical description of a regularized black hole and is based upon the idea that regularizing the singularity requires deviations from the Schwarzschild geometry which extend over horizon-sized scales, as well as maximally negative radial pressure as an equation of state. The frozen star has also been shown to be ultra-stable against perturbations; a feature that can be attributed to the equation of state and corresponds to this model mimicking a black hole in the limit $\hbar\to 0$ or, equivalently, the limit of infinite Newton's constant. Here, we ``defrost'' the frozen star by allowing its radial pressure to be perturbatively less negative than maximal. This modification to the equation of state is implemented by appropriately deforming the background metric so as to allow the frozen star to mimic a quantum black hole at finite $\hbar$ and Newton's constant. As a consequence, the defrosted star acquires a non-trivial spectrum of oscillatory perturbations. To show this, we first use the Cowling approximation to obtain generic equations for the energy density and pressure perturbations of a static, spherically symmetric background with an anisotropic fluid. The particular setting of a deformed frozen star is then considered, for which the dispersion relation is obtained to leading order in terms of the deviation from maximal pressure. The current results compare favorably with those obtained earlier for the collapsed polymer model, whose strongly non-classical interior is argued to provide a microscopic description of the frozen and defrosted star geometries.

##### 2.Energy condition bounds on $f(Q)$ model parameters in a curved FLRW universe

**Authors:**Ganesh Subramaniam, Avik De, Tee-How Loo, Yong Kheng Goh

**Abstract:** In this exclusive study of the modified $f(Q)$ theory of gravity in the open and closed type Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe model, we impose some constraints from the classical energy conditions. The viable range of parameter $\beta$ for two different $f(Q)$ models, $f(Q)=Q+\beta Q^2$ and $f(Q)=Q+\beta\sqrt{-Q}$, are analyzed in details and the related cosmological implications are discussed. Violation of effective strong energy condition is resulting into late-time acceleration of the Universe. Present observational values of Hubble parameter and deceleration parameter are used to constrain the parameters.

##### 3.Weyl-Lorentz-U(1)-invariant symmetric teleparallel gravity in three dimensions

**Authors:**Muzaffer Adak, Nese Ozdemir, Caglar Pala

**Abstract:** We consider a Weyl-Lorentz-U(1)-invariant gravity model written in terms of a scalar field, electromagnetic field and nonmetricity tensor in three dimensions. Firstly we obtain variational field equations from a Lagrangian. Then, we find some classes of circularly symmetric rotating solutions by exploiting the coincident gauge of symmetric teleparallel spacetime.

##### 4.Worldtube excision method for intermediate-mass-ratio inspirals: scalar-field model in 3+1 dimensions

**Authors:**Nikolas A. Wittek, Mekhi Dhesi, Leor Barack, Harald P. Pfeiffer, Adam Pound, Hannes R. Rüter, Marceline S. Bonilla, Nils Deppe, Lawrence E. Kidder, Prayush Kumar, Mark A. Scheel, William Throwe, Nils L. Vu

**Abstract:** Binary black hole simulations become increasingly more computationally expensive with smaller mass ratios, partly because of the longer evolution time, and partly because the lengthscale disparity dictates smaller time steps. The program initiated by Dhesi et al. (arXiv:2109.03531) explores a method for alleviating the scale disparity in simulations with mass ratios in the intermediate astrophysical range ($10^{-4} \lesssim q \lesssim 10^{-2}$), where purely perturbative methods may not be adequate. A region ("worldtube") much larger than the small black hole is excised from the numerical domain, and replaced with an analytical model approximating a tidally deformed black hole. Here we apply this idea to a toy model of a scalar charge in a fixed circular geodesic orbit around a Schwarzschild black hole, solving for the massless Klein-Gordon field. This is a first implementation of the worldtube excision method in full 3+1 dimensions. We demonstrate the accuracy and efficiency of the method, and discuss the steps towards applying it for evolving orbits and, ultimately, in the binary black-hole scenario. Our implementation is publicly accessible in the SpECTRE numerical relativity code.

##### 5.Spherically symmetric black hole spacetimes on hyperboloidal slices

**Authors:**Alex Vañó-Viñuales

**Abstract:** Gravitational radiation and some global properties of spacetimes can only be unambiguously measured at future null infinity. This motivates the interest in reaching it within simulations of coalescing compact objects, whose waveforms are extracted for gravitational wave modelling purposes. One promising method to include future null infinity in the numerical domain is the evolution on hyperboloidal slices: smooth spacelike slices that reach future null infinity. The main challenge in this approach is the treatment of the compactified asymptotic region at future null infinity. Evolution on a hyperboloidal slice of a spacetime including a BH entails an extra layer of difficulty, in part due to the finite coordinate distance between the BH and future null infinity. Spherical symmetry is considered here as simplest setup still encompassing the full complication of the treatment along the radial coordinate. First, the construction of constant-mean-curvature hyperboloidal trumpet slices for Schwarzschild and Reissner-Nordstroem BH spacetimes is reviewed from the point of view of the puncture approach. Then, the framework is set for solving hyperboloidal-adapted hyperbolic gauge conditions for stationary trumpet initial data, providing solutions for two specific sets of parameters. Finally, results of testing these initial data in evolution are presented.

##### 1.Thermal Radiation from an Electron with Schwarzschild-Planck Acceleration

**Authors:**Evgenii Ievlev, Michael R. R. Good, Eric V. Linder

**Abstract:** A charge accelerating in a straight line following the Schwarzschild-Planck moving mirror motion emits thermal radiation for a finite period. Such a mirror motion demonstrates quantum purity and serves as a direct analogy of a black hole with unitary evolution and complete evaporation. Extending the analog to classical electron motion, we derive the emission spectrum, power radiated, and finite total energy and particle count, with particular attention to the thermal radiation limit. This potentially opens the possibility of a laboratory analog of black hole evaporation.

##### 2.Anisotropic Solutions in Symmetric Teleparallel $f\left( Q\right)$-theory: Kantowski-Sachs and Bianchi III LRS Cosmologies

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

**Abstract:** We investigate the existence of anisotropic self-similar exact solutions in symmetric teleparallel $f\left( Q\right)$-theory. For the background geometry we consider the Kantowski-Sachs and the Locally Rotationally Symmetric Bianchi type III geometries. These two anisotropic spacetimes are of special interest because in the limit of isotropy they are related to the closed and open Friedmann--Lema\^{\i}tre--Robertson--Walker cosmologies respectively. For each spacetime there exist two distinct families of flat, symmetric connections, which share the symmetries of the spacetime. We present the field equations, and from them, we determine the functional form of the $f\left( Q\right)$ Lagrangian which yields self-similar solutions. We initially consider the vacuum case and subsequently we introduce a matter source in terms of a perfect fluid. Last but not least, we report some self-similar solutions corresponding to static spherically symmetric spacetimes.

##### 3.Strong Cosmic Censorship with Bounded Curvature

**Authors:**Moritz Reintjes

**Abstract:** In this paper we propose a weaker version of Penrose's much heeded Strong Cosmic Censorship (SCC) conjecture, asserting inextentability of maximal Cauchy developments by manifolds with Lipschitz continuous Lorentzian metrics and Riemann curvature bounded in $L^p$. Lipschitz continuity is the threshold regularity for causal structures, and curvature bounds rule out infinite tidal accelerations, arguing for physical significance of this weaker SCC conjecture. The main result of this paper, under the assumption that no extensions exist with higher connection regularity $W^{1,p}_\text{loc}$, proves in the affirmative this SCC conjecture with bounded curvature for $p$ sufficiently large, ($p>4$ with uniform bounds, $p>2$ without uniform bounds).

##### 4.Stability of relativistic tidal response against small potential modification

**Authors:**Takuya Katagiri, Hiroyuki Nakano, Kazuyuki Omukai

**Abstract:** The tidal response of compact objects in an inspiraling binary system is measured by a set of tidal Love and dissipation numbers imprinted in the gravitational waveforms. While a four-dimensional black hole in vacuum within General Relativity has vanishing Love numbers, a black hole in alternative theories of gravity can acquire non-vanishing Love numbers. The dissipation numbers may quantify Planckian corrections at the horizon scale. These properties will allow a test of classical theories of gravity in the strong-field regime with gravitational-wave observation. Since black holes are not in the exact vacuum environment in astrophysical situations, the following question arises: can the environment affect the tidal response? In this paper, we investigate the stability of the tidal response of a Schwarzschild black hole for frequency-dependent tidal-field perturbations against a small modification of the background. Our analysis relies on the scattering theory, which overcomes difficulties in defining the relativistic tidal Love numbers. The tidal Love and dissipation numbers can be extracted from the phase shift of sufficiently low-frequency scattering waves. We show that the tidal Love numbers are sensitive to the property of the modification. Therefore, we need careful consideration of the environment around the black hole in assessing the deviation of the underlying theory of gravity from General Relativity with the Love numbers. The modification has less impact on the dissipation numbers, indicating that quantifying the existence of the event horizon with them is not spoiled. We also demonstrate that in a composite system, i.e., a compact object with environmental effects, the Love and dissipation numbers are approximately determined by the sum of the numbers of each component.

##### 5.A Numerical Study of the Expanding Direction of $T^2$-Symmetric Spacetimes

**Authors:**Beverly K. Berger, James Isenberg, Adam Layne

**Abstract:** The asymptotic behavior of expanding, generic, $T^2$-Symmetric, vacuum spacetimes is examined via numerical simulations. After validation of the numerical methods, the properties of these generic spacetimes are explored and compared to non-generic subfamilies where proven results exist. The non-generic subfamilies within this class, including the Kasner, the Gowdy, the pseudo-homogeneous, and the $B=0$ spacetimes, all have known asymptotic behaviors in the expanding direction which have been determined either from the explicit solutions or using analytic methods. For the $B\ne 0$ spacetimes, the generic case within the $T^2$-Symmetric vacuum solutions, the asymptotic behavior has not been determined analytically. In this work, we use numerical simulations to explore the asymptotic behavior of the $B\ne 0$ spacetimes. Our results indicate that, for these generic spacetimes, the asymptotic behavior in the expanding direction differs from that seen in the non-generic subfamilies. In addition to differences in asymptotic power laws, an apparent quasi-periodic exchange of energy from one gravitational mode to the other for the generic non-polarized solutions is observed.

##### 6.Strong Gravitational Lensing of Gravitational Waves with TianQin

**Authors:**Xin-yi Lin, Jian-dong Zhang, Liang Dai, Shun-Jia Huang, Jianwei Mei

**Abstract:** When gravitational waves pass by a massive object on its way to the Earth, strong gravitational lensing effect will happen. Thus the GW signal will be amplified, deflected, and delayed in time. Through analysing the lensed GW waveform, physical properties of the lens can be inferred. On the other hand, neglecting lensing effects in the analysis of GW data may induce systematic errors in the estimating of source parameters. As a space-borne GW detector, TianQin will be launched in the 2030s. It is expected to detect dozens of MBHBs merger as far as z = 15, and thus will have high probability to detect at least one lensed event during the mission lifetime. In this article, we discuss the capability of TianQin to detect lensed MBHBs signals. Three lens models are considered in this work: the point mass model, the SIS model, and the NFW model. The sensitive frequency band for space-borne GW detectors is around milli-hertz, and the corresponding GW wavelength could be comparable to the lens gravitational length scale, which requires us to account for wave diffraction effects. In calculating lensed waveforms, we adopt the approximation of geometric optics at high frequencies to accelerate computation, while precisely evaluate the diffraction integral at low frequencies. Through a Fisher analysis, we analyse the accuracy to estimate the lens parameters. We find that the accuracy can reach to the level of 10^-3 for the mass of point mass and SIS lens, and to the level of 10^-5 for the density of NFW lens. We also assess the impact on the accurate of estimating the source parameters, and find that the improvement of the accuracy is dominated by the increasing of SNR.

##### 7.Efficient multi-timescale dynamics of precessing black-hole binaries

**Authors:**Davide Gerosa, Giulia Fumagalli, Matthew Mould, Giovanni Cavallotto, Diego Padilla Monroy, Daria Gangardt, Viola De Renzis

**Abstract:** We present analytical and numerical progress on black-hole binary spin precession at second post-Newtonian order using multi-timescale methods. In addition to the commonly used effective spin which acts as a constant of motion, we exploit the weighted spin difference and show that such reparametrization cures the coordinate singularity that affected the previous formulation for the case of equal-mass binaries. The dynamics on the precession timescale is written down in closed form in both coprecessing and inertial frames. Radiation-reaction can then be introduced in a quasi-adiabatic fashion such that, at least for binaries on quasi-circular orbits, gravitational inspirals reduce to solving a single ordinary differential equation. We provide a broad review of the resulting phenomenology and re-write the relevant physics in terms of the newly adopted parametrization. This includes the spin-orbit resonances, the up-down instability, spin propagation at past time infinity, and new precession estimators to be used in gravitational-wave astronomy. Our findings are implemented in version 2 of the public Python module PRECESSION. Performing a precession-averaged post-Newtonian evolution from/to arbitrarily large separation takes $\lesssim 0.1$ s on a single off-the-shelf processor. This allows for a wide variety of applications including propagating gravitational-wave posterior samples as well as population-synthesis predictions of astrophysical nature.

##### 8.Kasner-like description of spacelike singularities in spherically symmetric spacetimes with scalar matter

**Authors:**Warren Li

**Abstract:** We study the properties of spacelike singularities in spherically symmetric spacetimes obeying the Einstein equations, in the presence of matter. We consider in particular matter described by a scalar field, both in the presence of an electromagnetic field and without. We prove that if a spacelike singularity obeying several reasonable assumptions is formed, then the Hawking mass, the Kretschmann scalar, and the matter fields have inverse polynomial blow-up rates near the singularity that may be described precisely. Furthermore, one may view the resulting spacetime in the context of the BKL heuristics regarding space-like singularities in relativistic cosmology. In particular, near any point $p$ on the singular boundary in our spherically symmetric spacetime, we obtain a leading order BKL-type expansion, including a description of Kasner exponents associated to $p$. This provides a rigorous description of a detailed correspondence between Kasner-like singularities most often associated to the cosmological setting, and the singularities observed in (spherically symmetric) gravitational collapse. Moreover, we outline a program concerning the study of the stability and instability of spacelike singularities in the latter picture, both outside of spherical symmetry and within (where the electromagnetic field acts as a proxy for angular momentum) - in particular we signify the importance of cosmological phenomena including subcritical regimes and Kasner bounces in the collapse setting.