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

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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 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.

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Authors and Affiliations

  1. Physique-Mathématique, Universite de Mons-Hainaut, 7000, Mons, Belgium

    Yves Brihaye

  2. School of Engineering and Science, Jacobs University Bremen, 28759, Bremen, Germany

    Betti Hartmann

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  1. Yves Brihaye
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  2. Betti Hartmann
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ArXiv ePrint: 1112.6315

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Brihaye, Y., Hartmann, B. A scalar field instability of rotating and charged black holes in (4+1)-dimensional Anti-de Sitter space-time. J. High Energ. Phys. 2012, 50 (2012). https://doi.org/10.1007/JHEP03(2012)050

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