Hairy charged Gauss-Bonnet solitons and black holes

Abstract

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 and show that our solutions tend to their planar counterparts for large charges.

20 pages inlcuding 17 figures; v2: discussion on planar limit included, new figure added; accepted for publication in Phys. Rev. D

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• AdS solitons with conformal scalar hair
• Stationary Scalar Clouds Around Maximally Rotating Linear Dilaton Black Holes
• Minimal boson stars in 5 dimensions: classical instability and existence of ergoregions
• Formation of scalar hair on Gauss-Bonnet solitons and black holes
• Effectively four-dimensional spacetimes emerging from d=5 Einstein-Gauss-Bonnet Gravity
• Black rings with fourth dipole cause less hair loss
• Scalar Clouds and Quasinormal Modes