Thermodynamics and Stability of Hyperbolic Charged Black Holes

TL;DR

This paper investigates the thermodynamics and stability of hyperbolic charged black holes in Anti-de Sitter space, revealing conditions for global and local stability, phase transitions, and the influence of horizon topology across various dimensions.

Contribution

It provides a comprehensive analysis of hyperbolic charged black holes' thermodynamics in different ensembles, including stability criteria and phase transition conditions, extending understanding across multiple dimensions and supergravity theories.

Findings

Gibbs free energies are always negative, indicating global stability in the grand canonical ensemble.

Black holes can be locally unstable with negative heat capacity in certain phase space regions.

Hawking-Page phase transitions may occur, showing black holes are not always locally stable.

Abstract

In AdS space the black hole horizon can be a hypersurface with a positive, zero or negative constant curvature, resulting in different horizon topology. Thermodynamics and stability of black holes in AdS spaces are quite different for different horizon curvatures. In this paper we study thermodynamics and stability of hyperbolic charged black holes with negative constant curvature horizon in the grand canonical ensemble and canonical ensemble, respectively. They include hyperbolic Reissner-Nordstr\"om black holes in arbitrary dimensions and hyperbolic black holes in the D=5,4,7 gauged supergravities. It is found that the associated Gibbs free energies are always negative, which implies that these black hole solutions are globally stable and black hole phase is dominant in the grand canonical ensemble, but there is a region in the phase space where black hole is not locally thermodynamical stable with a negative heat capacity for a given gauge potential. In the canonical ensemble, the Helmholtz free energies are not always negative and heat capacities with fixed electric charge are not always positive, which indicates that the Hawking-Page phase transition may happen and black holes are not always locally thermodynamical stable.