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

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.