Existence of topological hairy dyons and dyonic black holes in anti-de Sitter 𝔰𝔲(N) Einstein-Yang-Mills theory - INSPIRE

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Existence of topological hairy dyons and dyonic black holes in anti-de Sitter 𝔰𝔲(N) Einstein-Yang-Mills theory

J. Erik Baxter
(
- Sheffield U.
)

Jul 19, 2015

48 pages

Published in:

J.Math.Phys. 57 (2016) 2, 022505

Published: Feb 2, 2016

e-Print:

1507.05314 [gr-qc]

DOI:

10.1063/1.4940337

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Abstract: (AIP)

We investigate dyonic black hole and dyon solutions of four-dimensional 𝔰𝔲(N) Einstein-Yang-Mills theory with a negative cosmological constant. We derive a set of field equations in this case, and prove the existence of non-trivial solutions to these equations for any integer N, with 2N − 2 gauge degrees of freedom. We do this by showing that solutions exist locally at infinity, and at the event horizon for black holes and the origin for solitons. We then prove that we can patch these solutions together regularly into global solutions that can be integrated arbitrarily far into the asymptotic regime. Our main result is to show that dyonic solutions exist in open sets in the parameter space, and hence that we can find non-trivial dyonic solutions in a number of regimes whose magnetic gauge fields have no zeros, which is likely important to the stability of the solutions.

Note:

48 pages

black hole: dyon
solution: stability
cosmological constant: negative
Einstein-Yang-Mills theory
SU(N)
gauge field theory
field equations
anti-de Sitter
topological
soliton

References(62)

Figures(0)

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