Abundant stable gauge field hair for black holes in anti-de Sitter space

TL;DR

This paper introduces new stable black hole solutions with gauge field hair in anti-de Sitter space, showing that black holes can support unlimited stable gauge field configurations.

Contribution

It provides explicit hairy black hole solutions in su(N) EYM theory in adS space, demonstrating their stability and the absence of an upper bound on stable gauge hair.

Findings

Existence of N+1 parameter black hole solutions with N-1 gauge degrees of freedom.

Stable solutions exist for all N with no zeros in gauge functions.

No upper limit on stable gauge field hair for black holes in adS.

Abstract

We present new hairy black hole solutions of su(N) Einstein-Yang-Mills theory (EYM) in asymptotically anti-de Sitter (adS) space. These black holes are described by N+1 independent parameters, and have N-1 independent gauge field degrees of freedom. Solutions in which all gauge field functions have no zeros exist for all N, and for sufficiently large (and negative) cosmological constant. At least some of these solutions are shown to be stable under classical, linear, spherically symmetric perturbations. Therefore there is no upper bound on the amount of stable gauge field hair with which a black hole in adS can be endowed.