Gravitational instability of Einstein-Gauss-Bonnet black holes under tensor mode perturbations

TL;DR

This paper investigates the stability of Einstein-Gauss-Bonnet black holes under tensor perturbations, deriving exact equations and identifying conditions for stability or instability across different dimensions and parameter choices.

Contribution

It provides the first detailed analysis of tensor mode stability for Einstein-Gauss-Bonnet black holes, including exact potential derivation and stability criteria in various dimensions.

Findings

Black holes in dimensions D ≠ 6 are stable for positive Gauss-Bonnet coupling.

In D=6, certain parameters lead to instability of positive mass black holes.

Stability depends critically on the spacetime dimension and Gauss-Bonnet coupling sign.

Abstract

We analyze the tensor mode perturbations of static, spherically symmetric solutions of the Einstein equations with a quadratic Gauss-Bonnet term in dimension $D > 4$. We show that the evolution equations for this type of perturbations can be cast in a Regge-Wheeler-Zerilli form, and obtain the exact potential for the corresponding Schr\"odinger-like stability equation. As an immediate application we prove that for $D \neq 6$ and $\alpha >0$, the sign choice for the Gauss-Bonnet coefficient suggested by string theory, all positive mass black holes of this type are stable. In the exceptional case $D =6$, we find a range of parameters where positive mass asymptotically flat black holes, with regular horizon, are unstable. This feature is found also in general for $\alpha < 0$.