General Relativity and Quantum Cosmology (gr-qc)

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.