On the existence of topological hairy black holes in $\mathfrak{su}(N)$ EYM theory with a negative cosmological constant

Abstract

We investigate the existence of black hole solutions of four dimensional $\mathfrak{su}(N)$ EYM theory with a negative cosmological constant. Our analysis differs from previous works in that we generalise the field equations to certain non-spherically symmetric spacetimes. We prove the existence of non-trivial solutions for any integer $N$, with $N-1$ gauge degrees of freedom. Specifically, we prove two results: existence of solutions for fixed values of the initial parameters and as $|\Lambda |\to \infty$, and existence of solutions for any $\Lambda <0$ in some neighbourhood of existing trivial solutions. In both cases we can prove the existence of `nodeless' solutions, i.e. such that all gauge field functions have no zeroes; this fact is of interest as we anticipate that some of them may be stable.

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Cited by in corpus (6)

• On the stability of soliton and hairy black hole solutions of $\mathfrak{su}(N)$ Einstein-Yang-Mills theory with a negative cosmological constant
• Existence of topological hairy dyons and dyonic black holes in anti-de Sitter SU(N) Einstein-Yang-Mills theory
• Black holes with $\mathfrak{su}(N)$ gauge field hair and superconducting horizons
• Topological black holes in $\mathfrak{su}(N)$ Einstein-Yang-Mills theory with a negative cosmological constant
• 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