Thermodynamic properties of asymptotically anti-de Sitter black holes in d=4 Einstein-Yang-Mills theory

TL;DR

This paper studies the thermodynamics of four-dimensional Einstein-Yang-Mills black holes in anti-de Sitter space, revealing stability properties and the dominance of abelian solutions over non-Abelian hair configurations.

Contribution

It provides a detailed analysis of the thermodynamic stability and phase structure of Einstein-Yang-Mills black holes with magnetic charge in AdS space, highlighting the dominance of abelian solutions.

Findings

Reissner-Nordström-AdS black holes can become unstable to non-Abelian hair formation.

Hairy black holes are not thermodynamically favored over abelian monopoles.

Thermodynamics of configurations with noninteger magnetic charge is discussed.

Abstract

We investigate the thermodynamics of spherically symmetric black hole solutions in a four-dimensional Einstein--Yang-Mills-SU(2) theory with a negative cosmological constant. Special attention is paid to configurations with a unit magnetic charge. We find that a set of Reissner-Nordstr\"om--Anti-de Sitter black holes can become unstable to forming non-Abelian hair. However, the hairy black holes are never thermodynamically favoured over the full set of abelian monopole solutions. The thermodynamics of the generic configurations possessing a noninteger magnetic charge is also discussed.