General Relativity and Gravitation最新文献

We construct a new class of ((n+1))-dimensional Lifshitz dilaton black brane solutions in the presence of the cubic quasitopological gravity for a flat boundary. The related action supports asymptotically Lifshitz solutions by applying some conditions which are used throughout the paper. We have to add a new boundary term and some new counterterms to the bulk action to have finite solutions. Then we define a finite stress tensor complex by which we can calculate the energy density of the quasitopological Lifshitz dilaton black brane. It is not possible to obtain analytical solutions, and so we use some expansions to probe -the behaviors of the functions, both near the horizon and, at the infinity. Combining the equations, we can attain a total constant along the coordinate r. At the horizon, this constant is proportional to the product of the temperature and the entropy and at the infinity, the total constant shows the energydensity of the quasitopological Lifshitz dilaton black brane. Therefore, we can reach a relation between the conserved quantities temperature, entropy and the energy density and get a smarr-type formula. Using the first law of thermodynamics, we can find a relation between the entropy and the temperature and then obtain the heat capacity. Our results show that the quasitopological Lifshitz dilaton black brane solutions are thermally stable for each positive value of the dynamical critiacl exponent, z.

We study zero and finite temperature static Bose-Einstein condensate (BEC) stars in the combined Rastall-Rainbow (RR) theory of gravity by considering different BEC equation of states (EoSs). We obtain the global properties of BEC stars by solving the modified Tolman-Oppenheimer-Volkoff equations of RR gravity with values of Rastall parameter (kappa ) and Rainbow function (Sigma ) chosen accordingly. We observe that the parameter (kappa ) has negligible effect on the maximum mass of the stars considered, whereas (Sigma ) alters it significantly, and increasing the value of (kappa ) beyond a certain limit results in unstable solutions for any value of (Sigma ). We report that the inclusion of temperature in our analysis expands the parameter space by including more values of (kappa ). However, temperature has negligible effect on the maximum mass of the stellar profiles in all the three theories. We have also studied the compactness and stability of the obtained stellar equilibria. We report that BEC stars satisfy various energy conditions within the range of (kappa ) and (Sigma ) taken in our paper. Further, we find that the maximum masses and radii of the stars within RR theory can have good agreement with the observational data on pulsars for all the EoSs considered and in particular, the Colpi-Wasserman-Shapiro EoS, which was ruled out in General Relativity (GR). We also find that, in contrast to the results of GR, BEC stars consistent with observations can be realised in the RR theory with smaller bosonic self-interaction strength.

This paper investigates the Joule-Thomson expansion for a five-dimensional neutral Gauss-Bonnet Anti-de Sitter black hole. Firstly, by taking Van der Waals gas as an example, we induce the definition of the Joule-Thomson coefficient and the inversion phenomena. One can give the T–P graph and the inversion curves. Then, we obtain the thermodynamic properties of the Gauss-Bonnet black hole and use the same way to get the T–P figure, which shows differences from Van der Waals gas and other black holes. To our surprise, we can’t observe its inversion phenomena. Due to this reason, we further studied the vanished inversion region and found that the electric charge plays an important role in this phenomenon. We analogy black hole charged and neutral, which get some interesting consequences. Finally, we make Legendre transition to Smarr relation and investigate whether the electric potential has the same result as the electric charge’s landscape. These results will uncover the inner interaction between the enthalpy and the electric charge during the Joule-Thomson process.

Quantum gravity has been baffling the theoretical physicist for decades now, both for its mathematical obscurity and phenomenological testing. Nevertheless, the new era of precision cosmology presents a promising avenue to test the effects of quantum gravity. In this study, we consider a bottom-up approach. Without resorting to any candidate quantum gravity, we invoke a generalized uncertainty principle (GUP) directly into the cosmological Hamiltonian for a universe sourced by a phantom scalar field with potential to study the evolution of the universe in a very early epoch. This is followed by a systematic analysis of the dynamics, both qualitatively and quantitatively. Our qualitative analysis shows that the introduction of GUP significantly alters the existence of fixed points for the potential considered in this paper. In addition, we confirm the existence of an inflationary phase and analyze the behavior of relevant cosmological parameters with respect to the strength of the GUP distortion.

We consider a homogeneous and isotropic spacetime having a space of positive curvature and study the cosmic evolution of dynamical vacuum energy. We utilize the dynamical system technique to study the existence of fixed points and their corresponding stability in model. The corresponding cosmological solutions describe late-time accelerating universe having decelerating era composed of radiation and matter-dominated phase. The numerical integration of autonomous system reveals that the cosmological solutions of dynamical vacuum energy model may describe the cosmic history of universe. As a consequence of the dynamical vacuum energy in closed Friedmann-Robertson-Walker model, the trajectories between fixed points in the phase space would also correspond to the bouncing and turnaround universe evolution.

Machine learning, particularly neural networks, has rapidly permeated most activities and work where data has a story to tell. Recently, deep learning has started to be used for solving differential equations with input from physics, also known as Physics-Informed Neural Network (PINNs). Physics-Informed Neural Networks (PINNs) applications in numerical relativity remain mostly unexplored. To remedy this situation, we present the first study of applying PINNs to solve in the time domain the Zerilli and the Regge-Wheeler equations for Schwarzschild black hole perturbations. The fundamental difference of our work with other PINN studies in black hole perturbations is that, instead of working in the frequency domain, we solve the equations in the time domain, an approach commonly used in numerical relativity to study initial value problems. To evaluate the accuracy of PINNs results, we compare the extracted quasi-normal modes with those obtained with finite difference methods. For comparable grid setups, the PINN results are similar to those from finite difference methods and differ from those obtained in the frequency domain by a few percent. As with other applications of PINNs for solving partial differential equations, the efficiency of neural networks over other methods emerges when applied to large dimensionality or high complexity problems. Our results support the viability of PINNs in numerical relativity, but more work is needed to assess their performance in problems such as the collision of compact objects.

We examine the black-hole limits of the family of static and spherically symmetric solutions of the Einstein field equations for polytropic matter, that was presented in a previous paper. This exploration is done in the asymptotic sub-regions of the allowed regions of the parameter planes of that family of solutions, for a few values of the polytropic index n, with the limitation that (n>1). These allowed regions were determined and discussed in some detail in another previous paper. The characteristics of these limits are examined and analyzed. We find that there are different types of black-hole limits, with specific characteristics involving the local temperature of the matter. We also find that the limits produce a very unexpected but specific type of spacetime geometry in the interior of the black holes, which we analyze in detail. Regarding the spatial part of the interior geometry, we show that in the black-hole limits there is a general collapse of all spatial distances to zero. Regarding the temporal part, there results an infinite overall red shift in the limits, with respect to the flat space at radial infinity, over the whole interior region. The analysis of the interior geometry leads to a very surprising connection with quantum-mechanical studies in the background metric of a naked Schwarzschild black hole. The nature of the solutions in the black-hole limits leads to the definition of a new type of singularity in General Relativity. We argue that the black-hole limits cannot actually be taken all the way to their ultimate conclusion, due to the fact that this would lead to the violation of some essential physical and mathematical conditions. These include questions of consistency of the solutions, questions involving infinite energies, and questions involving violations of the quantum behavior of matter. However, one can still approach these limiting situations to a very significant degree, from the physical standpoint, so that the limits can still be considered, at least for some purposes, as useful and simpler approximate representations of physically realizable configurations with rather extreme properties.

Hyperboloidal slices are spacelike slices that reach future null infinity. Their asymptotic behaviour is different from Cauchy slices, which are traditionally used in numerical relativity simulations. This work uses free evolution of the formally-singular conformally compactified Einstein equations in spherical symmetry. One way to construct gauge conditions suitable for this approach relies on building the gauge source functions from a time-independent background spacetime metric. This background reference metric is set using the height function approach to provide the correct asymptotics of hyperboloidal slices of Minkowski spacetime. The present objective is to study the effect of different choices of height function on hyperboloidal evolutions via the reference metrics used in the gauge conditions. A total of 10 reference metrics for Minkowski are explored, identifying some of their desired features. They include 3 hyperboloidal layer constructions, evolved with the non-linear Einstein equations for the first time. Focus is put on long-term numerical stability of the evolutions, including small initial gauge perturbations. The results will be relevant for future (puncture-type) hyperboloidal evolutions, 3D simulations and the development of coinciding Cauchy and hyperboloidal data, among other applications.

This paper is the initial part of a comprehensive study of spacetimes that admit the canonical forms of Killing tensor in General Relativity. The general scope of the study is to derive either new exact solutions of Einstein’s equations that exhibit hidden symmetries or to identify the hidden symmetries in already known spacetimes that may emerge during the resolution process. In this preliminary paper, we first introduce the canonical forms of Killing tensor, based on a geometrical approach to classify the canonical forms of symmetric 2-rank tensors, as postulated by R. V. Churchill. Subsequently, the derived integrability conditions of the canonical forms serve as additional equations transforming the under-determined system of equations, comprising of Einstein’s Field Equations and the Bianchi Identities (in vacuum with (Lambda )), into an over-determined one. Using a null rotation around the null tetrad frame we manage to simplify the system of equations to the point where the geometric characterization (Petrov Classification) of the extracted solutions can be performed and their null congruences can be characterized geometrically. Therein, we obtain multiple special algebraic solutions according to the Petrov classification (D, III, N, O) where some of them appeared to be new. The latter becomes possible since our analysis is embodied with the usage of the Newman-Penrose formalism of null tetrads.

We discuss the problem of singularity crossing in isotropic and anisotropic universes. We study at which conditions singularities can disappear in quantum cosmology and how quantum particles behave in the vicinity of singularities. Some attempts to develop general approach to the connection between the field reparametrization and the elimination of singularities is presented as well.