Spontaneous spherical symmetry breaking of black holes with resonant hair

TL;DR

This paper investigates the stability of black holes with resonant scalar hair, revealing their inherent dynamical instability and detailing how they decay into simpler configurations through non-spherical processes.

Contribution

It provides a comprehensive analysis of the instability mechanisms of black holes with scalar hair, including new decay channels and evidence of their generic nature across different models.

Findings

Black holes with resonant hair are dynamically unstable.

Instabilities lead to decay into a bosonic lump and a bald black hole or absorption.

Non-spherical dynamics are crucial for understanding their evolution.

Abstract

Black holes with resonant hair are static, spherical, electrically charged solutions of the Einstein-Maxwell-(gauged-)scalar system. Scalar self-interactions are mandatory for their existence. Initial dynamical studies restricted to spherical symmetry suggested stability; more recently, fully non-spherical dynamical studies revealed instabilities, at least for a particular class of self-interactions. Here, we provide a more detailed study of this instability together with a different decay channel, depending on the chosen solutions. Moreover, considering a second model, we provide evidence that the instabilities may be generic for different classes of self-interactions. We conclude these solutions are dynamically unstable and split into a bosonic lump and a bald black hole (via fission) or implode to the latter (via absorption). In both cases, the non-spherical dynamics seems to be key.