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

TL;DR

This paper constructs hairy black hole solutions in AdS$_4$ that emerge at the onset of superradiance, have higher entropy than Reissner-Nordstr"om black holes, and are potential endpoints of superradiant instability.

Contribution

It introduces a new class of hairy black holes in AdS$_4$ that merge with Reissner-Nordstr"om black holes at superradiance onset and analyzes their properties and stability.

Findings

Hairy black holes have higher entropy than Reissner-Nordstr"om black holes.

They are potential endpoints of charged superradiant instability.

Hairy black holes are related to solitons with zero horizon radius.

Abstract

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). 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-Nordstr\"om 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.