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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). 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Dias, Ramon Masachs","submitted_at":"2016-10-11T20:00:06Z","abstract_excerpt":"We construct hairy black hole solutions that merge with the anti-de Sitter (AdS$_4$) Reissner-Nordstr\\\"om 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-Nordstr\\\"om 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). 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