Hairy charged Gauss-Bonnet solitons and black holes

Details Hairy charged Gauss-Bonnet solitons and black holes Hairy charged Gauss-Bonnet solitons and black holes

2012-03-14

arxiv.org/abs/1203.3109v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages inlcuding 17 figures

Scientific paper

We study the stability of (4+1)-dimensional charged Gauss-Bonnet black holes and solitons. We observe an instability related to the condensation of a scalar field and construct explicit "hairy" black hole and soliton solutions of the full system of coupled field equations. We investigate the cases of a massless scalar field as well as that of a tachyonic scalar field. The solitons with scalar hair exist for a particular range of the charge and the gauge coupling. This range is such that for intermediate values of the gauge coupling a "forbidden band" of charges for the hairy solitons exists. We also discuss the behaviour of the black holes with scalar hair when changing the horizon radius and/or the gauge coupling and find that various scenarios at the approach of a limiting solution appear. One observation is that hairy Gauss-Bonnet black holes NEVER tend to a regular soliton solution in the limit of vanishing horizon radius. We also prove that extremal Gauss-Bonnet black holes can NOT carry massless or tachyonic scalar hair.

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