Abstract
We study small charged black holes in global AdS spacetime in the presence of a charged massless minimally coupled scalar field. In a certain parameter range these black holes suffer from well known superradiant instabilities. We demonstrate that the end point of the resultant tachyon condensation process is a hairy black hole which we construct analytically in a perturbative expansion in the black hole radius. At leading order our solution is a small undeformed RNAdS black hole immersed into a charged scalar condensate that fills the AdS ‘box’. These hairy black hole solutions appear in a two parameter family labelled by their mass and charge. Their mass is bounded from below by a function of their charge; at the lower bound a hairy black hole reduces to a regular horizon free soliton which can also be thought of as a nonlinear Bose condensate. We compute the microcanonical phase diagram of our system at small mass, and demonstrate that it exhibits a second order ‘phase transition’ between the RNAdS black hole and the hairy black hole phases.
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ArXiv ePrint: 1003.3232
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Basu, P., Bhattacharya, J., Bhattacharyya, S. et al. Small hairy black holes in global AdS spacetime. J. High Energ. Phys. 2010, 45 (2010). https://doi.org/10.1007/JHEP10(2010)045
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DOI: https://doi.org/10.1007/JHEP10(2010)045