General Relativity and Quantum Cosmology (gr-qc)

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.

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.}

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.

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.

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.

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.

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.

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....

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.