Extended phase space thermodynamics for black holes in a cavity

Abstract

In this paper, we extend the phase space of black holes enclosed by a spherical cavity of radius rB to include $$ V=4\pi {r}_B^3/3 $$ V = 4 π r B 3 / 3 as a thermodynamic volume. The thermodynamic behavior of Schwarzschild and Reissner-Nordstrom (RN) black holes is then investigated in the extended phase space. In a canonical ensemble at constant pressure, we find that the aforementioned thermodynamic behavior is remarkably similar to that of the anti-de Sitter (AdS) counterparts with the cosmological constant being interpreted as a pressure. Specifically, a first-order Hawking-Page-like phase transition occurs for a Schwarzschild black hole in a cavity. The phase structure of a RN black hole in a cavity shows a strong resemblance to that of the van der Waals fluid. We also display that the Smarr relation has the same expression in both AdS and cavity cases. Our results may provide a new perspective for the extended thermodynamics of AdS black holes by analogy with black holes in a cavity.

Scalarized Einstein–Maxwell-scalar black holes in a cavity

“…The results closely resemble those of the AdS counterparts for scalarized RN black holes. Recently, the phase space of black holes in a cavity has been extended by including a thermodynamic pressure and a thermodynamic volume [56], it is interesting to consider scalarized black holes enclosed by a cavity in the extended phase space. Moreover, one can study excited scalarized solutions since only the fundamental state was considered in this paper.…”

“…The phase structure and transitions of black holes in a cavity were shown to closely resemble that of the AdS counterparts for Schwarzschild black holes [52] and RN black holes [53][54][55]. Recently, it is found that the resemblance still exist in the extended phase space [56]. And it was discovered that Gauss-Bonnet black holes in a cavity also have quite similar phase structure and transitions to the AdS counterparts [57].…”

Thermodynamics and phase transition of BTZ black hole in a cavity

“…The phase structures of other thermodynamic systems such as black branes [5][6][7][8], boson stars [9] and hairy black holes [10,11] in cavity have caught many interests. Recently, the AdS space and cavity boundary conditions were compared based on various black holes such as nonlinear electrodynamics black hole [12], Gauss-Bonnet black hole [13], extended phase space black hole [14] and quintessence RN black hole [15], which showed great dissimilarities in phase transitions. However, these are all static black holes with dimensions no less than four.…”

Phase Structures and Transitions of Quintessence Surrounding RN Black Holes in a Grand Canonical Ensemble

“…Subsequently, it was extended to the case of a RN black hole which was considered in a grand canonical ensemble [19] and a canonical ensemble [20,21]. The thermodynamic phases of diverse black holes in a cavity were discussed in [22][23][24][25][26][27][28][29][30][31], which indicated that the Van de Waals-like phase transitions or the Hawking-Page-like phase transitions exist invariably except for some particular cases. The relationship between thermodynamic properties of black holes and their specific boundary conditions in different extended phase spaces was studied in [32].…”

“…Although many relevant work has been completed, there is no research that combines quintessential matter and cavity boundary condition. In addition, the discovery about the difference of phase structures of black holes between AdS space and Dirichlet cavity [28][29][30][31] also prompts us to investigate the phase structures of black holes from another perspective.…”