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

TL;DR

This paper investigates stable anti-de Sitter black holes with extensive gauge field hair in su(N) Einstein-Yang-Mills theory, demonstrating they can be characterized by mass and non-Abelian charges, supporting a generalized no-hair conjecture.

Contribution

It provides numerical and theoretical evidence that stable black holes in su(N) Einstein-Yang-Mills theory are characterized by a finite set of global charges, extending the no-hair conjecture to these solutions.

Findings

Stable black holes are characterized by mass and N-1 non-Abelian charges.

Numerical evidence for su(3) case shows fixed charges determine black hole configurations.

Large cosmological constant limit supports the no-hair conjecture for these black holes.

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).