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

Olga Kichakova,Jutta Kunz,Eugen Radu,Yasha Shnir

doi:10.1016/j.physletb.2015.05.052

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–Nordström–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.

Highlights

Black holes are non-perturbative objects whose existence appears to be an unavoidable consequence of general relativity
Some basic results derived at the semiclassical level, like the existence of Hawking radiation together with an intrinsic black holes (BHs) entropy are expected to be very basic features that any putative quantum theory of gravity will have to take into account
According to the antide Sitter (AdS)/CFT conjecture [2], BH solutions with AdS asymptotics would offer the possibility of probing the nonperturbative structure of some conformal field theories

Summary

Introduction

Black holes are non-perturbative objects whose existence appears to be an unavoidable consequence of general relativity (and its various extensions). BHs with non-Abelian (nA) hair in AdS background have been extensively studied, starting with the pioneering work [5] These EYM solutions possess a variety of interesting features which strongly contrast with those of the asymptotically flat spacetime counterparts in [6]. Stable BHs with a magnetic charge are known to exist even in the absence of a Higgs field (see [7] for a review of these solutions). Considering such configurations is a legitimate task, since the gauged supergravity models (of interest in AdS/CFT context) generically contain the EYM action as the basic building block. As we shall see, the thermodynamical properties of the solutions depend on the topology of the horizon, the case of spherical configurations being special

The solutions

The unit magnetic charge solutions

Solutions with a vanishing magnetic charge

The general case

Further remarks