Phase structures and transitions of Born–Infeld black holes in a grand canonical ensemble

Abstract

To make a Born-Infeld (BI) black hole thermally stable, we consider two types of boundary conditions, i.e., the asymptotically anti-de Sitter (AdS) space and a Dirichlet wall placed in the asymptotically flat space. The phase structures and transitions of these two types of BI black holes, namely BI-AdS black holes and BI black holes in a cavity, are investigated in a grand canonical ensemble, where the temperature and the potential are fixed. For BI-AdS black holes, the globally stable phases can be the thermal AdS space. For small values of the potential, there is a Hawking-Page-like first order phase transition between the BI-AdS black holes and the thermal-AdS space.However, the phase transition becomes zeroth order when the values of the potential are large enough. For BI black holes in a cavity, the globally stable phases can be a naked singularity or an extremal black hole with the horizon merging with the wall, which both are on the boundaries of the physical parameter region. The thermal flat space is never globally preferred. Besides a first order phase transition, there is a second order phase transition between the globally stable phases.Thus, it shows that the phase structures and transitions of BI black holes with these two different boundary conditions have several dissimilarities.

Scalarized Einstein–Maxwell-scalar black holes in a cavity

“…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]. However, it is shown that the phase structure of Born-Infeld black holes enclosed in a cavity has dissimilarities from that of Born-Infeld-AdS black holes [58,59]. Moreover, it is found that there exist significant differences between the thermodynamic geometry of RN black holes in a cavity and that of RN-AdS black holes [60], and some dissimilarities between the two cases also occur for validities of the second thermodynamic law and the weak cosmic censorship [61].…”

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].…”

Extended phase space thermodynamics for black holes in a cavity

“…However, we recently studied Born-Infeld black holes enclosed in a cavity in a canonical ensemble [56] and a grand canonical ensemble [57] and revealed that their phase structure has dissimilarities from that of Born-Infeld-AdS black holes. Moreover, contrary to the phase behavior, we found that there exist significant differences between the thermodynamic geometry of RN black holes in a cavity and that of RN-AdS black holes [58], and some dissimilarities between the two cases also occur for validities of the second thermodynamic law and the weak cosmic censorship [59].…”