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

  • J. Erik Baxter
Research Article

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. The work can be divided into two sections. In the first half, we use theorems of Wang’s to derive a new topologically general \(\mathfrak {su}(N)\)-invariant one-form connection which may serve as the ansatz for our gauge potential. The second half is devoted to proving the existence of non-trivial solutions to the field equations for any integer \(N\), with \(N-1\) gauge degrees of freedom. Specifically, we prove existence in two separate regimes: for fixed values of the initial parameters and as \(|\varLambda |\rightarrow \infty \); and for any \(\varLambda <0\), 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.

Keywords

Hairy black holes Topological black holes Anti-de Sitter  Einstein–Yang–Mills theory 

Notes

Acknowledgments

The author would like to thank Prof. E. Winstanley for many useful conversations and moral support; and Prof. H. P. Künzle for a very useful email exchange.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Harmer BuildingSheffield Hallam UniversitySheffieldUK

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