The Hawking–Page phase transitions in the extended phase space in the Gauss–Bonnet gravity

Abstract

In this paper, the Hawking-Page phase transitions between the black holes and thermal anti-de Sitter (AdS) space are studied with the Gauss-Bonnet term in the extended phase space, in which the varying cosmological constant plays the role of an effective thermodynamic pressure. The Gauss-Bonnet term exhibits its effects via introducing the corrections to the black hole entropy and Gibbs free energy. The global phase structures, especially the phase transition temperature T HP and the Gibbs free energy G, are systematically investigated, first for the Schwarzschild-AdS black holes and then for the charged and rotating AdS black holes in the grand canonical ensembles, with both analytical and numerical methods. It is found that there are terminal points in the coexistence lines, and T HP decreases at large electric potentials and angular velocities and also decreases with the Gauss-Bonnet coupling constant α.

Higher-curvature generalization of Eguchi-Hanson spaces

“…A similar behavior may be found for solutions whose Euclidean version corresponds to AlAdS gravitational instantons [51,52]. Thermodynamics and phase transitions of AlAdS solutions have also been studied in Lovelock theory, for instance in [53][54][55][56][57][58][59][60][61]. In the case of Eguchi-Hanson solutions, being intrinsically Euclidean and not AlAdS, the interpretation of the path integral results would be different.…”

The Hawking-Page-like Phase Transition from FRW Spacetime to McVittie Black Hole

“…The Gibbs free energy is a crucial thermodynamic function for studying the HP(-like) phase transitions [33,39,40,44]. For the McVittie black hole, the Gibbs free energy is given by…”

“…Below such a temperature the thermal AdS instead of the black hole becomes the stable one. This phase transition was later widely investigated in various black hole systems [34][35][36][37][38][39][40][41][42][43]. In this paper, we will follow the same criterion as [39,40,44,45] to determine the possibility of HP-like phase transition from FRW spacetime to McVittie black hole, that is, to determine their relative stability by comparing their Gibbs free energy with a fixed thermodynamic pressure.…”

“…This phase transition was later widely investigated in various black hole systems [34][35][36][37][38][39][40][41][42][43]. In this paper, we will follow the same criterion as [39,40,44,45] to determine the possibility of HP-like phase transition from FRW spacetime to McVittie black hole, that is, to determine their relative stability by comparing their Gibbs free energy with a fixed thermodynamic pressure. Our main conclusion is that such HP-like phase transition can happen if the thermodynamic pressure is positive.…”

On Rényi universality formula of charged flat black holes from Hawking-Page phase transition

“…[3,4], especially in the context of the AdS/CFT correspondence [5][6][7][8][9]. After the birth of the extended phase space notion in the AdS spacetime, this area was reexamined again with prolific outcomes [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. Moreover, it's largely understood that a black hole in an asymptotically flat space has negative heat capacity and is thus thermodynamically unstable.…”