Dressing a black hole with non-minimally coupled scalar field hair

TL;DR

This paper explores conditions under which black holes can have stable scalar field hair with non-minimal coupling, finding specific parameter regimes that allow stable hairy solutions.

Contribution

It demonstrates that stable scalar hair can exist on black holes only under certain negative cosmological constant and positive coupling conditions, expanding understanding of black hole scalar hair.

Findings

Stable hairy black hole solutions exist with negative cosmological constant and positive coupling.

Hair becomes unstable when the coupling constant exceeds a certain threshold.

No black hole hair is possible outside the identified parameter regimes.

Abstract

We investigate the possibility of dressing a four-dimensional black hole with classical scalar field hair which is non-minimally coupled to the space-time curvature. Our model includes a cosmological constant but no self-interaction potential for the scalar field. We are able to rule out black hole hair except when the cosmological constant is negative and the constant governing the coupling to the Ricci scalar curvature is positive. In this case, non-trivial hairy black hole solutions exist, at least some of which are linearly stable. However, when the coupling constant becomes too large, the black hole hair becomes unstable.