scholarly journals Revisit on the thermodynamic stability of Hořava–Lifshitz black hole

2018 ◽  
Vol 27 (04) ◽  
pp. 1850048
Author(s):  
Xudong Meng ◽  
Ruihong Wang
Keyword(s):  
Black Hole ◽  
Thermodynamic Properties ◽  
Thermodynamic Stability ◽  
Detailed Balance ◽  
De Sitter ◽  
Thermodynamic Variable ◽  
Detailed Balance Condition ◽  
First Law Of Thermodynamics ◽  
Balance Condition ◽  
Lifshitz Black Hole

We study the thermodynamic properties of the black hole derived in Hořava–Lifshitz (HL) gravity without the detailed-balance condition. The parameter [Formula: see text] in the HL black hole plays the same role as that of the electric charge in the Reissner–Nordström-anti-de Sitter (RN-AdS) black hole. By analogy, we treat the parameter [Formula: see text] as the thermodynamic variable and obtain the first law of thermodynamics for the HL black hole. Although the HL black hole and the RN-AdS black hole have the similar mass and temperature, due to their very different entropy, the two black holes have very different thermodynamic properties. By calculating the heat capacity and the free energy, we analyze the thermodynamic stability of the HL black hole.

scholarly journals Thermodynamic properties of black holes in de Sitter space

2016 ◽  
Vol 32 (02) ◽  
pp. 1750017 ◽  
Author(s):  
Huai-Fan Li ◽  
Meng-Sen Ma ◽  
Ya-Qin Ma
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Heat Capacity ◽  
Black Hole ◽  
Thermodynamic Properties ◽  
Thermodynamic Quantities ◽  
De Sitter ◽  
First Law Of Thermodynamics ◽  
Effective Temperatures ◽  
Sds Black Hole

We study the thermodynamic properties of Schwarzschild–de Sitter (SdS) black hole and Reissner–Nordström–de Sitter (RNdS) black hole in view of global and effective thermodynamic quantities. Making use of the effective first law of thermodynamics, we can derive the effective thermodynamic quantities of de Sitter black holes. It is found that these effective thermodynamic quantities also satisfy Smarr-like formula. Especially, the effective temperatures are nonzero in the Nariai limit. By calculating heat capacity and Gibbs free energy, we find SdS black hole is always thermodynamically stable and RNdS black hole may undergoes phase transition at some points.

scholarly journals The Critical Phenomena and Thermodynamics of the Reissner-Nordstrom-de Sitter Black Hole

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Ren Zhao ◽  
Mengsen Ma ◽  
Huihua Zhao ◽  
Lichun Zhang
Keyword(s):  
Black Hole ◽  
Critical Temperature ◽  
Thermodynamic Properties ◽  
Thermodynamic Stability ◽  
Critical Pressure ◽  
Black Hole Thermodynamics ◽  
Thermodynamic Quantities ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Sitter Spacetime

It is wellknown that there are two horizons for the Reissner-Nordstrom-de Sitter spacetime, namely, the black hole horizon and the cosmological one. Both horizons can usually seem to be two independent thermodynamic systems; however, the thermodynamic quantities on both horizons satisfy the laws of black hole thermodynamics and are not independent. In this paper by considering the relations between the two horizons we give the effective thermodynamic quantities in Reissner-Nordstrom-de Sitter spacetime. The thermodynamic properties of these effective quantities are analyzed; moreover, the critical temperature, critical pressure, and critical volume are obtained. We also discussed the thermodynamic stability of Reissner-Nordstrom-de Sitter spacetime.

scholarly journals f(R) TERM AND GEOMETRIC ORIGIN OF THE DARK SECTOR IN HOŘAVA–LIFSHITZ GRAVITY

2011 ◽  
Vol 26 (06) ◽  
pp. 387-398 ◽  
Author(s):  
ANZHONG WANG
Keyword(s):  
Detailed Balance ◽  
De Sitter ◽  
Dark Sector ◽  
Detailed Balance Condition ◽  
Balance Condition ◽  
Nonzero Curvature ◽  
Geometric Origin ◽  
The Universe ◽  
Scalar Perturbations ◽  
Scalar Mode

Inclusion of f(R) term in the action of Hořava–Lifshitz quantum gravity with projectability but without detailed balance condition is investigated, where R denotes the 3-spatial dimensional Ricci scalar. Conditions for the spin-0 graviton to be free of ghosts and instability are studied. The requirement that the theory reduces to general relativity in the IR makes the scalar mode unstable in the Minkowski background but stable in the de Sitter. It is remarkable that the dark sector, dark matter and dark energy, of the universe has a naturally geometric origin in such a setup. Bouncing universes can also be constructed. Scalar perturbations in the FRW backgrounds with nonzero curvature are also studied.

scholarly journals Black hole thermodynamics under the generalized uncertainty principle and doubly special relativity

2019 ◽  
Vol 2019 (8) ◽  
Author(s):  
E Maghsoodi ◽  
H Hassanabadi ◽  
Won Sang Chung
Keyword(s):  
Black Hole ◽  
Thermodynamic Properties ◽  
Special Relativity ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Black Hole Thermodynamics ◽  
De Sitter ◽  
Doubly Special Relativity ◽  
Heuristic Analysis ◽  
Horizon Case

Abstract We investigate the effect of the generalized uncertainty principle on the thermodynamic properties of the topological charged black hole in anti-de Sitter space within the framework of doubly special relativity. Our study is based on a heuristic analysis of a particle which is captured by the black hole. We obtain some thermodynamic properties of the black hole including temperature, entropy, and heat capacity in the spherical horizon case.

Convergence of Markov chains in the relative supremum norm

2000 ◽  
Vol 37 (4) ◽  
pp. 1074-1083 ◽  
Author(s):  
Lars Holden
Keyword(s):  
Markov Chain ◽  
Detailed Balance ◽  
Continuity Condition ◽  
Supremum Norm ◽  
Weak Continuity ◽  
Norm Convergence ◽  
Detailed Balance Condition ◽  
Balance Condition ◽  
Qualitative Understanding ◽  
Doeblin Condition

It is proved that the strong Doeblin condition (i.e., ps(x,y) ≥ asπ(y) for all x,y in the state space) implies convergence in the relative supremum norm for a general Markov chain. The convergence is geometric with rate (1 - as)1/s. If the detailed balance condition and a weak continuity condition are satisfied, then the strong Doeblin condition is equivalent to convergence in the relative supremum norm. Convergence in other norms under weaker assumptions is proved. The results give qualitative understanding of the convergence.

Convergence to the equilibrium for the Pauli equation without detailed balance condition

2005 ◽  
Vol 341 (1) ◽  
pp. 5-10 ◽  
Author(s):  
Naoufel Ben Abdallah ◽  
Miguel Escobedo ◽  
Stéphane Mischler
Keyword(s):  
Detailed Balance ◽  
Pauli Equation ◽  
Detailed Balance Condition ◽  
Balance Condition

scholarly journals Existence condition and phase transition of Reissner–Nordström–de Sitter black hole

2014 ◽  
Vol 29 (09) ◽  
pp. 1450050 ◽  
Author(s):  
Meng-Sen Ma ◽  
Hui-Hua Zhao ◽  
Li-Chun Zhang ◽  
Ren Zhao
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Thermodynamic Properties ◽  
Electric Charge ◽  
Transition Point ◽  
Existence Condition ◽  
Phase Transition Point ◽  
Black Hole Horizon ◽  
Cosmological Horizon ◽  
De Sitter

After introducing the connection between the black hole horizon and the cosmological horizon, we discuss the thermodynamic properties of Reissner–Nordström–de Sitter (RN–dS) space–time. We present the condition under which RN–dS black hole can exist. Employing Ehrenfest' classification, we conclude that the phase transition of RN–dS black hole is the second-order one. The position of the phase transition point is irrelevant to the electric charge of the system. It only depends on the ratio of the black hole horizon and the cosmological horizon.

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