Abstract
We first discuss the thermodynamics of a Born-Infeld (BI) black hole enclosed in a finite spherical cavity. A canonical ensemble is considered, which means that the temperature and the charge on the wall of the cavity are fixed. After the free energy is obtained by computing the Euclidean action, it shows that the first law of thermodynamics is satisfied at the locally stationary points of the free energy. The phase structure and transition in various regions of the parameter space are then investigated. In the region where the BI electrodynamics has weak nonlinearities, Hawking-Page-like and van der Waals-like phase transitions occur, and a tricritical point appears. In the region where the BI electrodynamics has strong enough nonlinearities, only Hawking-Page-like phase transitions occur. The phase diagram of a BI black hole in a cavity can have dissimilarity from that of a BI black hole using asymptotically anti-de Sitter boundary conditions. The dissimilarity may stem from a lack of an appropriate reference state with the same charge and temperature for the BI-AdS black hole.
Highlights
JHEP07(2019)002 was found that the nonlinear dynamical evolution of a charged black hole in a cavity could end in a quasi-local hairy black hole
We find that Hawking-Page-like and van der Waals-like phase transitions can occur while there is no reentrant phase transition
In the first part of this paper, we calculated the Euclidean action of a BI black hole in a finite spherical cavity and investigated the corresponding thermodynamic behavior in a canonical ensemble
Summary
We consider a BI black hole inside a cavity, on the boundary of which the temperature and charge are fixed. On a (3 + 1) dimensional spacetime manifold M with a time-like boundary ∂M, the action of gravity coupled to a BI electromagnetic field Aμ, is given by. Note that the second term in Ssurf is included to keep the charge fixed on ∂M, instead of the potential [70]. On the boundary of the cavity ∂M at r = rB, the gauge potential measured on ∂M with respect to the horizon at r = r+ is. Where the blueshift factor 1/ f (rB) relates At to the proper orthonormal frame component of the potential one-form [12], and we fix the gauge field At (r) at the horizon to be zero
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