Stability of black holes in Einstein-charged scalar field theory in a cavity

TL;DR

This paper investigates whether black holes with scalar hair in Einstein-charged scalar field theory can be stable end-states of superradiant instabilities, providing evidence that such hairy solutions are linearly stable.

Contribution

It introduces a family of static charged scalar-hairy black hole solutions and demonstrates their linear stability, suggesting they could be the final state of superradiant instability.

Findings

Hairy black hole solutions are stable under linear perturbations.

Stable hairy solutions may be the end-point of superradiant instability.

Numerical evidence supports stability of single-node hairy solutions.

Abstract

Can a black hole that suffers a superradiant instability evolve towards a 'hairy' configuration which is stable? We address this question in the context of Einstein-charged scalar field theory. First, we describe a family of static black hole solutions which possess charged scalar-field hair confined within a mirror-like boundary. Next, we derive a set of equations which govern the linear, spherically symmetric perturbations of these hairy solutions. We present numerical evidence which suggests that, unlike the vacuum solutions, the (single-node) hairy solutions are stable under linear perturbations. Thus, it is plausible that stable hairy black holes represent the end-point of the superradiant instability of electrically-charged Reissner-Nordstrom black holes in a cavity; we outline ways to explore this hypothesis.