Phase diagram of the charged black hole bomb system

TL;DR

This paper maps the phase diagram of charged black holes with scalar hair confined in a cavity, revealing new stable solutions and their relation to boson stars, with implications for black hole stability and end states.

Contribution

It presents the first detailed phase diagram of static hairy black holes in Einstein-Maxwell-Scalar theory with boundary conditions, identifying critical charges and stability features.

Findings

Hairy black holes have higher entropy than Reissner-Nordström black holes at the same mass and charge.

Existence of four critical scalar charges marking qualitative changes in the phase diagram.

Hairy black holes connect to boson star solutions when the horizon radius approaches zero.

Abstract

We find the phase diagram of solutions of the charged black hole bomb system. In particular, we find the static hairy black holes of Einstein-Maxwell-Scalar theory confined in a Minkowski box. We impose boundary conditions such that the scalar field vanishes at and outside a cavity of constant radius. These hairy black holes are asymptotically flat with a scalar condensate floating above the horizon. We identify four critical scalar charges which mark significant changes in the qualitative features of the phase diagram. When they coexist, hairy black holes always have higher entropy than the Reissner-Nordstr\"om black hole with the same quasilocal mass and charge. So hairy black holes are natural candidates for the endpoint of the superradiant/near-horizon instabilities of the black hole bomb system. We also relate hairy black holes to the boson stars of the theory. When it has a zero horizon radius limit, the hairy black hole family terminates on the boson star family. Finally, we find the Israel surface tensor of the box required to confine the scalar condensate and that it can obey suitable energy conditions.