On the mechanical stability of asymptotically flat black holes with minimally coupled scalar hair

TL;DR

This paper demonstrates that certain asymptotically flat black holes with scalar hair are linearly unstable, with a finite number of unstable modes whose frequencies can be arbitrarily small, impacting their physical viability.

Contribution

It provides the first analysis of linear stability for these black holes, revealing their mode instability and characterizing the nature of their unstable modes.

Findings

Black holes with scalar hair are linearly unstable.

Number of unstable modes is finite.

Unstable mode frequencies can be arbitrarily small.

Abstract

We show that the asymptotically flat hairy black holes, solutions of the Einstein field equations minimally coupled to a scalar field, previously discovered by one of us, present mode instability against linear radial perturbations. It is also shown that the number of unstable modes is finite and their frequencies can be made arbitrarily small.