arXiv subjects

Ren Zhao

Publications and source records attributed to Ren Zhao.

At least 37 records · Page 2Linked to original sources

arXiv2017

Entropy of higher-dimensional charged de Sitter black holes and phase transition

From a new perspective, we discuss the thermodynamic entropy of $n+2$-dimensional Reissner-Nordström-de Sitter(RNdS) black hole and analyze the phase transition of the effective thermodynamic system. Considering the correlations between the black hole event horizon and the cosmological horizon, we conjecture that the total entropy of the RNdS black hole should contain an extra term besides the sum of the entropies of the two horizons. In the lukewarm case, the effective temperature of the RNdS black hole is the same as that of the black hole horizon and the cosmological horizon. Under this condition, we obtain the extra contribution to the total entropy. With the corrected entropy, we derive other effective thermodynamic quantities and analyze the phase transition of the RNdS black hole in analogy to the usual thermodynamic system.

gr-qc↗

arXiv2017

Noncommutative geometry inspired black holes in Rastall gravity

Under two different metric ansatzes, the noncommutative geometry inspired black holes (NCBH) in the framework of Rastall gravity are derived and analyzed. We consider the fluid-type matter with the Gaussian-distribution smeared mass density. Taking a Schwarzschild-like metric ansatz, it is shown that the noncommutative geometry inspired Schwarzschild black hole (NCSBH) in Rastall gravity, unlike its counterpart in general relativity (GR), is not a regular black hole. It has at most one event horizon. After showing a finite maximal temperature, the black hole will leave behind a point-like massive remnant at zero temperature. Considering a more general metric ansatz and a special equation of state of the matter, we also find a regular NCBH in Rastall gravity, which has a similar geometric structure and temperature to that of NCSBH in GR.

hep-th↗

arXiv2017

Thermodynamics of de Sitter black hole in massive gravity

In this paper, by taking de Sitter space-time as a thermodynamic system, we study the equivalent thermodynamic quantities of de Sitter black hole in massive gravity, and furthermore obtain the equivalent thermodynamic quantities of the space-time. Our results show that the entropy of this type of space-time takes the same form as that in Reissner-Nordstrom-de Sitter space-time, which lays a solid foundation for deeply understanding the universal thermodynamic characteristics of de Sitter space-time in the future. Moreover, our analysis indicates that the equivalent thermodynamic quantities and relevant parameters play a very important role, especially in the investigation of the stability and evolution of de Sitter space-time.

hep-th↗

arXiv2017

Thermodynamics and critical behaviors of topological dS black holes with nonlinear source

We discuss black hole solutions of Einstein gravity in presence of nonlinear electrodynamics in dS spacetime. Considering prescribed entropy, thermodynamic volume of dS spacetime, We investigate properties of the effective thermodynamic quantities under influence of nonlinearity parameter $α$. They show a similar phase transition and criticality properties with that of black holes in AdS spacetime. And the nonlinearity parameter $α$ combined with electric charge is found to have effects on the phase structure. By the Ehrenfest equations we prove the critical phase transition is a second order equilibrium transition.

hep-th↗

arXiv2017

Phase transition and thermodynamic stability of topological black holes in Hořava-Lifshitz gravity

On the basis of horizon thermodynamics, we study the thermodynamic stability and $P-V$ criticality of topological black holes constructed in Hořava-Lifshitz (HL) gravity without the detailed-balance condition (with general $ε$). In the framework of horizon thermodynamics, we do not need the concrete black hole solution (the metric function) and the concrete matter fields. It is shown that the HL black hole for $k=0$ is always thermodynamically stable. For $k=1$, the thermodynamic behaviors and $P-V$ criticality of the HL black hole are similar to those of RN-AdS black hole for some $ε$. For $k=-1$, the temperature is classified into six types by their different features. Among them, we mainly focus on the type with triply degenerate thermodynamic state. It is also shown that there is a "thermodynamic singularity" for the $k=-1$ HL black hole, where the temperature and Gibbs free energy both diverge apart from a special pressure $P_s$.

hep-th↗

arXiv2017

The thermodynamic relationship between the RN-AdS black holes and the RN black hole in canonical ensemble

In this paper, by analyzing the thermodynamic properties of charged AdS black hole and asymptotically flat space-time charged black hole in the vicinity of the critical point, we establish the correspondence between the thermodynamic parameters of asymptotically flat space-time and nonasymptotically flat space-time, based on the equality of black hole horizon area in the two different space-time. The relationship between the cavity radius (which is introduced in the study of asymptotically flat space-time charged black holes) and the cosmological constant (which is introduced in the study of nonasymptotically flat space-time) is determined. The establishment of the correspondence between the thermodynamics parameters in two different space-time is beneficial to the mutual promotion of different time-space black hole research, which is helpful to understand the thermodynamics and quantumproperties of black hole in space-time.

hep-th↗

arXiv2016

$Q-Φ$ criticality in the extended phase space of $(n+1)$-dimensional RN-AdS black holes

In order to achieve a deeper understanding of gravity theories, it is important to further investigate the thermodynamic properties of black hole at the critical point, besides the phase transition and critical behaviors. In this paper, by using Maxwell's equal area law, we choose $T,Q,Φ$ as the state parameters and study the phase equilibrium problem of general $(n+1)$-dimensional RN-AdS black holes thermodynamic system. The boundary of the two-phase coexistence region and its isotherm and isopotential lines are presented, which may provide theoretical foundation for studying the phase transition and phase structure of black hole systems.

hep-th↗

arXiv2016

Entropy of Reissner-Nordström-de Sitter black hole

Based on the consideration that the black hole horizon and the cosmological horizon of Reissner-Nordström black hole in de Sitter space are not independent each other, we conjecture the total entropy of the system should have an extra term contributed from the entanglement between the two horizons, except for the sum of the two horizon entropies. Making use of the globally effective first law and the effective thermodynamic quantities, we derive the total entropy and find that it will diverge as the two horizons tends to coincide.

gr-qc↗

arXiv2016

Phase Transition and Clapeyon Equation of Black Hole in Higher Dimensional AdS Spacetime

By Maxwell equal area law we study the phase transition in higher dimensional Anti-de Sitter (AdS) Reissner-Nordström (RN) black hole and Kerr black hole in this paper. The coexisting region of the two phases involved in the phase transition is found and the coexisting curves are shown in $P-T$ figures. We also analytically investigate the parameters which affect the coexisting curves. To better compare with ordinary thermodynamic systems, the Clapeyon equation is derived for higher dimensional AdS black holes. This paper can help to deepen the understanding of the phase transition and phase structure of AdS black holes.

hep-th↗

arXiv2016

Thermodynamic stability of black holes surrounded by quintessence

We study the thermodynamic stabilities of uncharged and charged black holes surrounded by quintessence (BHQ) by means of effective thermodynamic quantities. When the state parameter of quintessence $ω_q$ is appropriately chosen, the structures of BHQ are something like that of black holes in de Sitter space. Constructing the effective first law of thermodynamics in two different ways, we can derive the effective thermodynamic quantities of BHQ. Especially, these effective thermodynamic quantities also satisfy Smarr-like formulae. It is found that the uncharged BHQ is always thermodynamically unstable due to negative heat capacity, while for the charged BHQ there are phase transitions of the second order. We also show that there is a great deal of difference on the thermodynamic properties and critical behaviors of BHQ between the two ways we employed.

gr-qc↗

arXiv2016

The phase transition of higher dimensional Charged black holes

In this paper,we have studied phase transitions of higher dimensional charge black hole with spherical symmetry. we calculated the local energy and local temperature, and find that these state parameters satisfy the first law of thermodynamics. We analyze the critical behavior of black hole thermodynamic system by taking state parameters $(Q,Φ)$ of black hole thermodynamic system, in accordance with considering to the state parameters $(P,V)$ of Van der Waals system respectively. we obtain the critical point of black hole thermodynamic system, and find the critical point is independent of the dual independent variables we selected. This result for asymptotically flat space is consistent with that for AdS spacetime, and is intrinsic property of black hole thermodynamic system.

gr-qc↗

arXiv2015

Two-phase equilibrium properties in charged topological dilaton AdS black holes

In this paper we discuss phase transition of the charged topological dilaton AdS black holes by Maxwell equal area law. The two phases involved in the phase transition could be coexist and we depict the coexistence region in $P-v$ diagrams. The two-phase equilibrium curves in $P-T$ diagrams are plotted, the Clapeyron equation for the black hole is derived, and the latent heat of isothermal phase transition is investigated. We also analyze of the parameters of the black hole that have an effect on the two phases coexistence. The results show that the black hole may go through a small-large phase transition similar to those of usual non-gravity thermodynamic systems.

gr-qc↗

arXiv2015

Stability of black holes based on horizon thermodynamics

On the basis of horizon thermodynamics we study the thermodynamic stability of black holes constructed in general relativity and Gauss-Bonnet gravity. In the framework of horizon thermodynamics there are only five thermodynamic variables $E,P,V,T,S$. It is not necessary to consider concrete matter fields, which may contribute to the pressure of black hole thermodynamic system. In non-vacuum cases, we can derive the equation of state, $P=P(V,T)$. According to the requirements of stable equilibrium in conventional thermodynamics, we start from these thermodynamic variables to calculate the heat capacity at constant pressure and Gibbs free energy and analyze the local and global thermodynamic stability of black holes. It is shown that $P>0$ is the necessary condition for black holes in general relativity to be thermodynamically stable, however this condition cannot be satisfied by many black holes in general relativity. For black hole in Gauss-Bonnet gravity negative pressure can be feasible, but only local stable black hole exists in this case.

gr-qc↗

arXiv2014

Corrected form of the first law of thermodynamics for regular black holes

We show by explicit computations that there is a superficial inconsistency between the conventional first law of black hole thermodynamics and Bekenstein-Hawking area law for three types of regular black holes. The corrected form of the first law for these regular black holes is given. The derivation relies on the general structure of the energy-momentum tensor of the matter fields. When the black hole mass parameter $M$ is included in the energy-momentum tensor, the conventional form of the first law should be modified with an extra factor. In this case, the black hole mass $M$ can no longer be considered as the internal energy of the regular black holes.

gr-qc↗

arXiv2014

Phase transition of the higher dimensional charged Gauss-Bonnet black hole in de Sitter spacetime

We study the phase transition of charged Gauss-Bonnet-de Sitter (GB-dS) black hole. For black holes in de Sitter spacetime, there is not only black hole horizon, but also the cosmological horizon. The thermodynamic quantities on the both horizons satisfy the first law of the black hole thermodynamics, respectively; moreover, there are additional connections between them. Using the effective temperature approach, we obtained the effective thermodynamic quantities of charged GB-dS black hole. According to Ehrenfest classification, we calculate some response functions and plot their figures, from which one can see that the spacetime undergoes a second-order phase transition at the critical point. It is shown that the critical values of effective temperature and pressure decrease with the increase of the value of GB parameter $α$.

gr-qc↗

arXiv2014

Superconvergent Two-grid Methods For Elliptic Eigenvalue Problems

Some numerical algorithms for elliptic eigenvalue problems are proposed, analyzed, and numerically tested. The methods combine advantages of the two-grid algorithm, two-space method, the shifted inverse power method, and the polynomial preserving recovery technique . Our new algorithms compare favorably with some existing methods and enjoy superconvergence property.

math.NA↗

arXiv2014

Hessian Recovery for Finite Element Methods

In this article, we propose and analyze an effective Hessian recovery strategy for the Lagrangian finite element of arbitrary order $k$. We prove that the proposed Hessian recovery preserves polynomials of degree $k+1$ on general unstructured meshes and superconverges at rate $O(h^k)$ on mildly structured meshes. In addition, the method preserves polynomials of degree $k+2$ on translation invariant meshes and produces a symmetric Hessian matrix when the sampling points for recovery are selected with symmetry. Numerical examples are presented to support our theoretical results.

math.NA↗

arXiv2014

Thermodynamics of phase transition in higher dimensional Reissner-Nordström-de Sitter black hole

It is well known that there are black hole and the cosmological horizons for the Reissner-Nordström-de Sitter spacetime. Although the thermodynamic quantities on the horizons are not irrelevant, they satisfy the laws of black hole thermodynamics respectively. In this paper by considering the relations between the two horizons we give the effective thermodynamic quantities in $(n+2)$-dimensional Reissner-Nordström-de Sitter spacetime. The thermodynamic properties of these effective quantities are analyzed, moreover, the critical temperature, critical pressure and critical volume are obtained. We carry out an analytical check of Ehrenfest equations and prove that both Ehrenfest equations are satisfied. So the spacetime undergoes a second order phase transition at the critical point. This result is consistent with the nature of liquid--gas phase transition at the critical point, hence deepening the understanding of the analogy of charged dS spacetime and liquid--gas systems.

gr-qc↗