Charged Black Hole in a Canonical Ensemble

TL;DR

This paper analyzes the thermodynamics and phase structure of a charged black hole in a cavity with fixed charge and temperature, comparing it to AdS boundary conditions to explore holographic principles.

Contribution

It derives the phase structure and stability of charged black holes in a cavity, highlighting similarities with AdS boundary conditions and implications for holography.

Findings

Black hole thermodynamics in a cavity shows extensive similarities to AdS cases.

Stable and unstable equilibrium states are characterized.

Boundary conditions influence thermodynamic properties more than the specific spacetime geometry.

Abstract

We consider the thermodynamics of a charged black hole enclosed in a cavity. The charge in the cavity and the temperature at the walls are fixed so that we have a canonical ensemble. We derive the phase structure and stability of black hole equilibrium states. We compare our results to that of other work which uses asymptotically anti-de Sitter boundary conditions to define the thermodynamics. The thermodynamic properties have extensive similarities which suggest that the idea of AdS holography is more dependent on the existence of the boundary than on the exact details of asymptotically AdS metrics.