Small hairy black holes in global AdS spacetime

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.

Phases of global AdS black holes

“…Here too, the number of phases remain three. A Chandrasekhar-like instability for AdS black holes was found in [8,9] when the q was below some bound. In our case, that bound corresponds to q = 1.…”

“…We can also evaluate the q at which the two curves intersect and it is found to be around ≈ 0.9. We can think of the boson star instability as a proxy for the bulk instability of AdS black holes when the black hole is small (this is sometimes called superradiant instability, [8,9]). It will be interesting to see if the interplay between these two types of instabilities leads to a quantum critical phase transition for the hairy extremal solutions.…”

“…The aim of this paper is to investigate this question in some detail. Unlike previous works in this direction (see [8][9][10][11] ), which considered…”

A scalar field instability of rotating and charged black holes in (4+1)-dimensional Anti-de Sitter space-time

“…The existence of solitons in global AdS was discovered in [29], where a perturbative approach was taken. In [28] it was shown that solitons can have arbitrarily large charge for large enough gauge coupling, while for small gauge coupling the solutions exhibit a spiralling behaviour towards a critical solution with finite charge and mass.…”

Black hole bombs and explosions: from astrophysics to particle physics

“…Such possible end-states were discussed in Refs. [56,63,64,65]. Some examples of rotating solutions with scalar hair were explicitly constructed in Refs.…”