Thermodynamics of Gauss–Bonnet–de Sitter black holes

Abstract

We investigate the thermodynamics of Gauss-Bonnet black holes in asymptotically de Sitter spacetimes embedded in an isothermal cavity, via a Euclidean action approach. We consider both charged and uncharged black holes, working in the extended phase space where the cosmological constant is treated as a thermodynamic pressure. We examine the phase structure of these black holes through their free energy. In the uncharged case, we find both Hawking-Page and small-to-large black hole phase transitions, whose character depends on the sign of the Gauss-Bonnet coupling. In the charged case, we demonstrate the presence of a swallowtube, signaling a compact region in phase space where a small-to-large black hole transition occurs.

Extended Phase Space Thermodynamics for Black Holes in a Cavity

“…Additionally, it has been proposed [60] that the holographic dual of T T deformed CFT 2 is a finite region of AdS 3 with the wall at finite radial distance, which makes studying properties of black holes in a cavity more attractive. Note that thermodynamics and critical behavior of de Sitter black holes in a cavity were recently investigated in [61][62][63].…”

Thermodynamics of de Sitter Black Holes with Conformally Coupled Scalar Fields

“…The variations above are done with all other parameters held fixed, possibly necessitating the inclusion of extra terms to account for the dependency of β on those parameters 3 . This kind of approach has been used to study thermodynamic aspects of successively more exotic spacetimes (particularly with de Sitter asymptotics), such as neutral and charged de Sitter black holes [34,35], Born-Infeld black holes [36], and Gauss-Bonnet black holes [37], demonstrating a wide variety of thermodynamic phenomena.…”

“…Fixing the temperature at the cavity allows the black hole to achieve equilibrium, permitting the study of equilibrium thermodynamics. Upon taking the extended thermodynamic phase space into account, new phenomena emerge for charged de Sitter black holes, such as swallowtubes and analogues of the familiar Hawking-Page (HP), small-large, and reentrant phase transitions exhibited by AdS black holes [35][36][37].…”

Extended phase space thermodynamics for black holes in a cavity

“…Additionally, it has been proposed [60] that the holographic dual of TT deformed CFT 2 is a finite region of AdS 3 with the wall at finite radial distance, which makes studying properties of black holes in a cavity more attractive. Note that thermodynamics and critical behavior of de Sitter black holes in a cavity were recently investigated in [61][62][63].…”