Critical phenomena of charged de Sitter black holes in cavities

Abstract

We examine the thermodynamic behaviour of four-dimensional charged and uncharged de Sitter black holes enclosed in an isothermal cavity, in the extended phase space where the cosmological constant is treated as a thermodynamic pressure. We demonstrate the presence of a novel pressure-dependent phase transition in a compact region of phase space that does not appear in asymptotically anti-de Sitter black holes, and find a highly non-linear equation of state that does not lead to the usual interpretation of a van der Waals fluid.

Thermodynamics of Gauss–Bonnet–de Sitter black holes

“…Unlike the typical 'swallowtail' behaviour seen in asymptotically AdS black holes (see for example [68]), the free energy here forms a tube in F − T − P space, as shown in Figure 7. This 'swallowtube' behaviour, first observed in [27], is in stark contrast to the swallowtails that arise in black hole systems without cavities. In those systems, there is only a maximum pressure P max below which the phase transition is present.…”

“…As in [24][25][26][27][28], we shall impose that the black hole resides in a perfectly reflecting cavity which necessitates a Dirichlet boundary condition at the location of the cavity. The temperature of the cavity will be held fixed and will generically be different than the temperature associated with the cosmological horizon.…”

“…The cavity approach was first applied to de Sitter black holes in [26], though that analysis did not consider aspects of the extended thermodynamics. Recently generalizations of this approach to include considerations of the extended thermodynamics have been used to uncover examples of compact van der Waals-like transitions for charged de Sitter black holes [27] and re-entrant phase transitions for de Sitter black holes with nonlinear electrodynamics [28].…”

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

“…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].…”

Thermodynamic geometry of AdS black holes and black holes in a cavity

“…Boson stars and hairy black holes in a cavity were considered in [27][28][29][30], which showed that the phase structure of the gravity system in a cavity is strikingly similar to that of holographic superconductors in the AdS gravity. Moreover, the thermodynamic and critical behavior of de Sitter black holes in a cavity were investigated in the extended phase space [31]. Recently, we studied Born-Infeld black holes enclosed in a cavity in a canonical ensemble [32] and a grand canonical ensemble [33], respectively, and found that their phase structure has dissimilarities from that of Born-Infeld-AdS black holes.…”