Do stringy corrections stabilize coloured black holes?

TL;DR

This paper investigates the stability of coloured black holes with stringy corrections, finding that such corrections do not eliminate certain instabilities, and that stability varies depending on charge and horizon size.

Contribution

It provides a detailed stability analysis of Einstein-Yang-Mills-Dilaton black holes with Gauss-Bonnet corrections, revealing persistent instabilities and stability conditions across different black hole types.

Findings

Stringy corrections do not remove sphaleronic instabilities.

Coloured black holes are unstable in the large horizon limit.

Neutral and electrically charged black holes are stable under small perturbations.

Abstract

We consider hairy black hole solutions of Einstein-Yang-Mills-Dilaton theory, coupled to a Gauss-Bonnet curvature term, and we study their stability under small, spacetime-dependent perturbations. We demonstrate that the stringy corrections do not remove the sphaleronic instabilities of the coloured black holes with the number of unstable modes being equal to the number of nodes of the background gauge function. In the gravitational sector, and in the limit of an infinitely large horizon, the coloured black holes are also found to be unstable. Similar behaviour is exhibited by the magnetically charged black holes while the bulk of the neutral black holes are proven to be stable under small, gauge-dependent perturbations. Finally, the electrically charged black holes are found to be characterized only by the existence of a gravitational sector of perturbations. As in the case of neutral black holes, we demonstrate that for the bulk of electrically charged black holes no unstable modes arise in this sector.