Thermodynamics of Reissner-Nordstrom-anti-de Sitter black holes in the grand canonical ensemble

TL;DR

This paper analyzes the thermodynamic behavior of Reissner-Nordstrom-anti-de Sitter black holes within a grand canonical ensemble, revealing conditions for stability and the existence of instantons with negative heat capacity.

Contribution

It applies York's formalism to compute thermodynamic quantities of these black holes in a finite cavity, exploring stability conditions and instanton solutions.

Findings

Stable black hole solutions exist under specific boundary conditions.

Instantons with negative heat capacity are identified.

Thermodynamic properties depend on cavity radius, temperature, and potential.

Abstract

The thermodynamical properties of the Reissner-Nordstr\"om-anti-de Sitter black hole in the grand canonical ensemble are investigated using York's formalism. The black hole is enclosed in a cavity with finite radius where the temperature and electrostatic potential are fixed. The boundary conditions allow us to compute the relevant thermodynamical quantities, e.g. thermal energy, entropy and charge. The stability conditions imply that there are thermodynamically stable black hole solutions, under certain conditions. Instantons with negative heat capacity are also found.