Hairy charged Gauss-Bonnet solitons and black holes

TL;DR

This paper explores the stability and existence of hairy charged Gauss-Bonnet black holes and solitons in five dimensions, revealing new solutions with scalar hair and analyzing their properties and limitations.

Contribution

It constructs explicit hairy black hole and soliton solutions in Gauss-Bonnet gravity, analyzing their stability, parameter ranges, and limiting behaviors, which were previously unexplored.

Findings

Hairy black holes and solitons exist within specific charge and gauge coupling ranges.

Hairy solutions do not tend to regular solitons as horizon radius approaches zero.

Extremal Gauss-Bonnet black holes cannot support massless or tachyonic scalar hair.

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.