A unified phase transition picture of the charged topological black hole in Hořava-Lifshitz gravity

Abstract

Aiming at a unified phase transition picture of the charged topological black hole in Hořava-Lifshitz gravity, we investigate this issue not only in canonical ensemble with the fixed charge case but also in grand-canonical ensemble with the fixed potential case. We firstly perform the standard analysis of the specific heat, the free energy and the Gibbs potential, and then study its geometrothermodynamics. It is shown that the local phase transition points not only witness the divergence of the specific heat, but also witness the minimum temperature and the maximum free energy or Gibbs potential. They also witness the divergence of the corresponding thermodynamic scalar curvature. No matter which ensemble is chosen, the metric constructed can successfully produce the behavior of the thermodynamic interaction and phase transition structure while other metrics failed to predict the phase transition point of the charged topological black hole in former literature. In grand-canonical ensemble, we have discovered the phase transition which has not been reported before. It is similar to the canonical ensemble in which the phase transition only takes place when k = −1. But it also has its unique characteristics that the location of the phase transition point depends on the value of potential, which is different from the canonical ensemble where the phase transition point is independent of the parameters. After an analytical check of Ehrenfest scheme, we find that the new phase transition is a second order one. It is also found that the thermodynamics of the black hole in Horava-Lifshitz gravity is quite different from that in Einstein gravity. 1

Critical behavior of Born-Infeld AdS black holes in the extended phase space thermodynamics

“…More interesting discoveries were obtained for the charged AdS black holes [6,7], where it was found that a first order small black hole and big black hole phase transition is allowed which is superficially analogous to a liquid-gas phase transition of the van der Waals fluid. This superficial reminiscence was also observed in other AdS backgrounds [8][9][10][11][12][13][14][15][16][17][18][19][20].…”

Thermodynamic instability of topological black holes in Gauss-Bonnet gravity with a generalized electrodynamics

“…To do so, one can use the method that was introduced in [18] and can use geometrothermodynamics to solve ensemble dependency of the system [18,19].…”

Phase transition and thermodynamic stability in extended phase space and charged Hořava–Lifshitz black holes

“…It can be treated as a candidate for a quantum gravity theory. In the last few years, its black hole solutions and the corresponding thermodynamics have been studied in literature [25][26][27][28][29][30][31][32][33][34][35].…”

“…Hořava-Lifshitz gravity is a UV complete non-relativistic power-counting renormalizable theory of gravity proposed by Hořava [23,24], which reduces to Einstein's general relativity in the IR limit. Its black hole solutions were presented in [25][26][27][28] and the thermodynamics of these black holes has * mb.jahani@iasbs.ac.ir † n riazi@sbu.ac.ir been investigated in [29][30][31][32][33][34][35]. The authors of [34] study the thermodynamics and phase transition of charged Hořava-Lifshitz black holes in non-extended phase space.…”