Black Strings in Gauss-Bonnet Theory are Unstable

TL;DR

This paper demonstrates that black strings in Gauss-Bonnet theory in seven dimensions are unstable due to s-wave modes, supporting the Gubser-Mitra conjecture and highlighting their thermal instability.

Contribution

It provides the first analytic evidence of instability in Gauss-Bonnet black strings, deriving a master equation for perturbations and linking instability to thermodynamic properties.

Findings

Unstable s-wave modes found in seven-dimensional Gauss-Bonnet black strings.

Master equation admits bounded solutions indicating exponential growth of perturbations.

Results support the Gubser-Mitra conjecture relating classical and thermodynamic stability.

Abstract

We report the existence of unstable, s-wave modes, for black strings in Gauss-Bonnet theory (which is quadratic in the curvature) in seven dimensions. This theory admits analytic uniform black strings that in the transverse section are black holes of the same Gauss-Bonnet theory in six dimensions. All the components of the perturbation can be written in terms of a single one and its derivatives. For this latter component we find a master equation which admits bounded solutions provided the characteristic time of the exponential growth of the perturbation is related with the wave number along the extra direction, as it occurs in General-Relativity. It is known that these configurations suffer from a thermal instability, and therefore the results presented here provide evidence for the Gubser-Mitra conjecture in the context of Gauss-Bonnet theory. Due to the non-triviality of the curvature of the background, all the components of the metric perturbation appear in the linearized equations. As it occurs for spherical black holes, these black strings should be obtained as the short distance $r<<\alpha^{1/2}$ limit of the black string solution of Einstein-Gauss-Bonnet theory, which is not know analytically, where $\alpha$ is the Gauss-Bonnet coupling.