Thermodynamics of horizons: de Sitter black holes and reentrant phase transitions

Abstract

In this paper we propose a straightforward method for understanding the thermodynamics of black holes in de Sitter space, one that will allow us to study these black holes in a way that is analogous to the anti-de Sitter case. As per usual, we formulate separate thermodynamic first laws for each horizon present in the spacetime, and study their thermodynamics as if they were independent systems characterized by their own temperature. That these systems are not entirely independent and various thermodynamic quantities in them are in fact 'correlated' is reflected by the fact that their thermodynamics can be captured by a single Gibbs free energy-like thermodynamic potential. This quantity contains information about possible phase transitions in the system and allows us to uncover a rich phase structure for de Sitter black holes. In particular, we discover reentrant phase transitions for Kerr-dS black holes in six dimensions, a phenomenon recently observed for their six dimensional AdS cousins.

Thermodynamics of Gauss–Bonnet–de Sitter black holes

“…Most of these investigations pertain to anti-de Sitter black holes, while the case of de Sitter black holes has seen comparatively little development [17][18][19]. Notwithstanding the inherent difficulties, there are good reasons for exploring these ideas in the de Sitter realm.…”

An exploration of the black hole entropy via the Weyl tensor

“…the Schwarzschild solution with a positive cosmological constant) is not a well-defined issue [30][31][32][33][34][35][36], and we skip the corresponding discussion in the present paper.…”

Critical phenomena of Born-Infeld-de Sitter black holes in cavities

“…These considerations motivate a study of black hole thermodynamics in asymptotically de Sitter spacetimes [11][12][13]. New issues arise due to the presence of a cosmological horizon, and the subject is presently not well understood.…”

“…One solution is to consider an ensemble where the temperature is specified at a finite boundary [18]. This 'isothermal cavity' allows the black hole to come to a stable thermodynamic equilibrium, and has been used to understand the critical behaviour of charged de Sitter black holes both in the standard phase space [19], as well as the extended phase space [20] (where the cosmological constant acts as a thermodynamic pressure [13]). In the former case a Hawking-Page-like phase transition in both the asymptotically flat and de Sitter cases is observed [19].…”