A scalar field instability of rotating and charged black holes in (4+1)-dimensional Anti-de Sitter space-time

Abstract

We study the stability of static as well as of rotating and charged black holes in (4+1)-dimensional Anti-de Sitter space-time which possess spherical horizon topology. We observe a non-linear instability related to the condensation of a charged, tachyonic scalar field and construct "hairy" black hole solutions of the full system of coupled Einstein, Maxwell and scalar field equations. We observe that the limiting solution for small horizon radius is either a hairy soliton solution or a singular solution that is not a regular extremal solution. Within the context of the gauge/gravity duality the condensation of the scalar field describes a holographic conductor/superconductor phase transition on the surface of a sphere.

16 pages including 8 figures, v2: discussion on soliton solutions extended; v3: matches version accepted for publication in JHEP

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Cited by in corpus (7)

• Logarithmic corrections of charged hairy black hole in (2+1) dimension
• Rotating Hairy Black Holes in AdS${}_5\times$S${}^5$
• Spinning gauged boson stars in anti-de Sitter spacetime
• Hairy charged Gauss-Bonnet solitons and black holes
• AdS solitons with conformal scalar hair
• Formation of scalar hair on Gauss-Bonnet solitons and black holes
• The temperature and entropy corrections on the charged hairy black holes