Exact formation of hairy planar black holes

TL;DR

This paper derives exact static and dynamical hairy black hole solutions in Einstein-scalar gravity with AdS asymptotics, revealing two classes of collapse behaviors and their stability properties.

Contribution

It provides the first exact dynamical solutions for black hole formation in Einstein-scalar theories with AdS asymptotics, including novel collapse scenarios.

Findings

Two classes of collapse solutions identified

One class evolves from naked singularity to black hole, unstable

Another class evolves from AdS vacuum to black hole, non-linearly unstable

Abstract

We consider Einstein gravity minimally coupled to a scalar field with a given potential in general dimensions. We obtain large classes of static hairy planar black holes which are asymptotic to AdS space-times. In particular, for a special case $\mu=(n-2)/2$, we obtain new classes of exact dynamical solutions describing black holes formation. We find there are two classes of collapse solutions. The first class solutions describe the evolution start from AdS space-time with a naked singularity at the origin. The space-time is linearly unstable and evolves into stationary black hole states even under small perturbation. The second class solutions describe the space-time spontaneously evolves from AdS vacua into stationary black hole states undergoing non-linear instability. We also discuss the global properties of all these dynamical solutions.