Abstract
We investigate the phase space of topological black hole solutions of su(N) Einstein–Yang–Mills theory in anti-de Sitter space with a purely magnetic gauge potential. The gauge field is described by N−1 magnetic gauge field functions ωj, j=1,…,N−1. For su(2) gauge group, the function ω1 has no zeros. This is no longer the case when we consider a larger gauge group. The phase space of topological black holes is considerably simpler than for the corresponding spherically symmetric black holes, but for N>2 and a flat event horizon, there exist solutions where at least one of the ωj functions has one or more zeros. For most of the solutions, all the ωj functions have no zeros, and at least some of these are linearly stable.
Highlights
Many properties of black holes in asymptotically anti-de Sitter space-time are rather different from those of black holes in asymptotically flat space-time
A natural question is whether there exist analogues of the purely magnetic, spherically symmetric black holes in su(N) EYM in anti-de Sitter (adS) with nonspherical event horizon topology
We show the region of the parameter space for which there are nontrivial topological black hole solutions and label these solutions by the quantities n j, with n j being the number of zeros of the magnetic gauge field function ω j
Summary
Many properties of black holes in asymptotically anti-de Sitter (adS) space-time are rather different from those of black holes in asymptotically flat space-time. There exist stable, spherically symmetric, asymptotically adS, black hole solutions of su(2) EYM with a negative cosmological constant [15,16,17]. A natural question is whether there exist analogues of the purely magnetic, spherically symmetric black holes in su(N) EYM in adS with nonspherical event horizon topology. This question was answered in the affirmative [24], in two regimes: (a) for a negative cosmological constant with sufficiently large magnitude and (b) in a neighbourhood of an embedded su(2) solution.
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