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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'.
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