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Physical Review D

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Hairy charged Gauss-Bonnet solitons and black holes

Yves Brihaye^1,* and Betti Hartmann^2,†

¹Physique-Mathématique, Universite de Mons-Hainaut, 7000 Mons, Belgium
²School of Engineering and Science, Jacobs University Bremen, 28759 Bremen, Germany

^*yves.brihaye@umons.ac.be
^†b.hartmann@jacobs-university.de

Phys. Rev. D 85, 124024 – Published 14 June, 2012

DOI: https://doi.org/10.1103/PhysRevD.85.124024

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 behavior 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.

Article Text

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