Scalar solitons and the microscopic entropy of hairy black holes in three dimensions

Abstract

General Relativity coupled to a self-interacting scalar field in three dimensions is shown to admit exact analytic soliton solutions, such that the metric and the scalar field are regular everywhere. Since the scalar field acquires slow fall-off at infinity, the soliton describes an asymptotically AdS spacetime in a relaxed sense as compared with the one of Brown and Henneaux. Nevertheless, the asymptotic symmetry group remains to be the conformal group, and the algebra of the canonical generators possesses the standard central extension. For this class of asymptotic behavior, the theory also admits hairy black holes which raises some puzzles concerning an holographic derivation of their entropy à la Strominger. Since the soliton is devoid of integration constants, it has a fixed (negative) mass, and it can be naturally regarded as the ground state of the "hairy sector", for which the scalar field is switched on. This assumption allows to exactly reproduce the semiclassical hairy black hole entropy from the asymptotic growth of the number of states by means of Cardy formula. Particularly useful is expressing the asymptotic growth of the number of states only in terms of the spectrum of the Virasoro operators without making any explicit reference to the central charges.

17 pages, 1 figure

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• Gribov ambiguity in asymptotically AdS three-dimensional gravity
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• Black Holes with Scalar Hair in Three Dimensions
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• Rotating $(2+1)$-dimensional Black Holes in Einstein-Maxwell-Dilaton Theory
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• Gravity coupled to a scalar field from a Chern-Simons action: describing rotating hairy black holes and solitons with gauge fields
• Hairy black holes in AdS with Robin boundary conditions
• Microscopic entropy of static black holes in 3d Lovelock gravities
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• Regular AdS${}_3$ black holes from regularized Gauss-Bonnet coupling