Instability of a four-dimensional de Sitter black hole with a conformally coupled scalar field

TL;DR

This paper investigates the stability of new four-dimensional de Sitter black hole solutions with conformally coupled scalar fields, finding that most are unstable, including both neutral and charged cases.

Contribution

It provides the first detailed stability analysis of these novel black hole solutions with a positive cosmological constant and conformal scalar coupling.

Findings

Neutral black holes are always unstable.

Most charged black holes are unstable across the parameter space.

Numerical evidence suggests remaining solutions are also unstable.

Abstract

We study the stability of new neutral and electrically charged four-dimensional black hole solutions of Einstein's equations with a positive cosmological constant and conformally coupled scalar field. The neutral black holes are always unstable. The charged black holes are also shown analytically to be unstable for the vast majority of the parameter space of solutions, and we argue using numerical techniques that the configurations corresponding to the remainder of the parameter space are also unstable.