Topological black holes in $\mathfrak{su}(N)$ Einstein-Yang-Mills theory with a negative cosmological constant

Abstract

We investigate the phase space of topological black hole solutions of $\mathfrak{su}(N)$ 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 ${\omega }_j$, $j=1,\dots ,N-1$. For $\mathfrak{su}(2)$ gauge group, the function ${\omega }_1$ 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 ${\omega }_j$ functions has one or more zeros. For most of the solutions, all the ${\omega }_j$ functions have no zeros, and at least some of these are linearly stable.

7 pages, 3 figures, minor changes, references added, matches published version

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Cited by in corpus (7)

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• On the stability of soliton and hairy black hole solutions of $\mathfrak{su}(N)$ Einstein-Yang-Mills theory with a negative cosmological constant
• Black holes with $\mathfrak{su}(N)$ gauge field hair and superconducting horizons
• Analytic non-Abelian gravitating solitons in the Einstein-Yang-Mills-Higgs theory and transitions between them
• On the global existence of spherically symmetric hairy black holes and solitons in anti-de Sitter Einstein-Yang-Mills theories with compact semisimple gauge groups
• On the existence of topological dyons and dyonic black holes in anti-de Sitter Einstein-Yang-Mills theories with compact semisimple gauge groups
• Dyonic black holes in $\mathfrak{su}(\infty )$ anti-de Sitter Einstein-Yang-Mills theory, characterised by an infinite set of global charges