Hairy black holes and the endpoint of AdS${}_4$ charged superradiance

Abstract

We construct hairy black hole solutions that merge with the anti-de Sitter (AdS${}_4$) Reissner-Nordström black hole at the onset of superradiance. These hairy black holes have, for a given mass and charge, higher entropy than the corresponding AdS${}_4$-Reissner-Nordström black hole. Therefore, they are natural candidates for the endpoint of the charged superradiant instability. On the other hand, hairy black holes never dominate the canonical and grand-canonical ensembles. The zero-horizon radius of the hairy black holes is a soliton (i.e. a boson star under a gauge transformation). We construct our solutions perturbatively, for small mass and charge, so that the properties of hairy black holes can be used to testify and compare with the endpoint of initial value simulations. We further discuss the near-horizon scalar condensation instability which is also present in global AdS${}_4$-Reissner-Nordström black holes. We highlight the different nature of the near-horizon and superradiant instabilities and that hairy black holes ultimately exist because of the non-linear instability of AdS.

41 pages, 6 figures. v2: Minor changes to match published version

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Cited by in corpus (3)

• The large charge expansion and AdS/CFT
• Large-Charge Limit of AdS Boson Stars with Mixed Boundary Conditions
• Gravitational systems in asymptotically anti-de Sitter space-times