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

Glueball condensates as holographic duals of supersymmetricQ-balls and boson stars

“…Qualitatively similar results exist when describing insulator/superfluid phase transitions with non-vanishing superfluid velocity [29]. Charged solitons in global AdS have also recently been studied in 4 dimensions [34] as well as in 5 dimensions [35,36].…”

Formation of scalar hair on Gauss-Bonnet solitons and black holes

“…This has already been considered in [34]. Here we point out further important details in the pattern of solutions.…”

“…It was pointed out that the solutions tend to their planar counterparts for large charges since in that case the solutions can become comparable in size to the AdS radius. The influence of the Gauss-Bonnet corrections on the instability of these solutions has been discussed in [34].…”

“…We study the case of solitons in more detail and point out further details in comparison to [34]. Moreover, we also discuss static and rotating Gauss-Bonnet black holes with and without scalar hair.…”

Charged dilatonic black holes in gravity’s rainbow

“…The late-time evolution of a self-interacting scalar field for a dilatonic black hole has also been analyzed [142]. It may be noted that the scalar hair for charged Gauss-Bonnet black holes have been studied [143]. It has been demonstrated that the solitons with scalar hair exist for a particular range of the charge and the gauge coupling.…”