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

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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
(
- Sheffield Hallam U.
)

Mar 2, 2014

35 pages

Published in:

Gen.Rel.Grav. 47 (2015) 1, 1829

Published: Nov 28, 2014

e-Print:

1403.0171 [gr-qc]

DOI:

10.1007/s10714-014-1829-5

View in:

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Abstract: (Springer)

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.

Hairy black holes
Topological black holes
Anti-de Sitter
Einstein-Yang-Mills theory
cosmological constant: negative
black hole: hair
Einstein-Yang-Mills theory
black hole: topological
stability

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