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A scalar field instability of rotating and charged black holes in (4+1)-dimensional Anti-de Sitter space-time. (English) Zbl 1309.83060

Summary: 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 an instability related to the condensation of a charged, tachyonic scalar field and construct “hairy” black hole solutions of the full non-linear 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.

MSC:

83C57 Black holes
83C15 Exact solutions to problems in general relativity and gravitational theory
83C22 Einstein-Maxwell equations
35C08 Soliton solutions
81T13 Yang-Mills and other gauge theories in quantum field theory
81V17 Gravitational interaction in quantum theory
82D55 Statistical mechanics of superconductors

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