Characterizing asymptotically anti-de Sitter black holes with abundant stable gauge field hair

Abstract

In the light of the "no-hair" conjecture, we revisit stable black holes in su(N) Einstein-Yang-Mills theory with a negative cosmological constant. These black holes are endowed with copious amounts of gauge field hair, and we address the question of whether these black holes can be uniquely characterized by their mass and a set of global non-Abelian charges defined far from the black hole. For the su(3) case, we present numerical evidence that stable black hole configurations are fixed by their mass and two non-Abelian charges. For general N, we argue that the mass and N-1 non-Abelian charges are sufficient to characterize large stable black holes, in keeping with the spirit of the "no-hair" conjecture, at least in the limit of very large magnitude cosmological constant and for a subspace containing stable black holes (and possibly some unstable ones as well).

33 pages, 13 figures, minor changes

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• On the existence of dyons and dyonic black holes in Einstein-Yang-Mills theory
• On the stability of soliton and hairy black hole solutions of $\mathfrak{su}(N)$ Einstein-Yang-Mills theory with a negative cosmological constant
• On the stability of dyons and dyonic black holes in Einstein-Yang-Mills theory
• Black holes with $\mathfrak{su}(N)$ gauge field hair and superconducting horizons
• Solitons and hairy black holes in Einstein-non-Abelian-Proca theory in anti-de Sitter space-time
• On the existence of topological hairy black holes in $\mathfrak{su}(N)$ EYM theory with a negative cosmological constant
• A black hole solution of higher-dimensional Weyl-Yang-Kaluza-Klein theory
• Dyonic black holes in $\mathfrak{su}(\infty )$ anti-de Sitter Einstein-Yang-Mills theory, characterised by an infinite set of global charges