Linear stability of Einstein-Gauss-Bonnet static spacetimes. Part II: vector and scalar perturbations

TL;DR

This paper investigates the linear stability of Einstein-Gauss-Bonnet static spacetimes, focusing on vector and scalar perturbations, revealing stability for vector modes but potential instabilities for scalar modes in certain black hole configurations.

Contribution

It extends previous work by analyzing vector and scalar perturbations, showing vector stability and identifying possible scalar instabilities due to Gauss-Bonnet corrections.

Findings

Vector perturbations are stable under linear analysis.

Scalar perturbations can cause instabilities in spherical black holes with Gauss-Bonnet terms.

The S-deformation method effectively analyzes vector perturbations.

Abstract

We study the stability under linear perturbations of a class of static solutions of Einstein-Gauss-Bonnet gravity in $D=n+2$ dimensions with spatial slices of the form $\Sigma_{\k}^n \times {\mathbb R}^+$, $\Sigma_{\k}^n$ an $n-$manifold of constant curvature $\k$. Linear perturbations for this class of space-times can be generally classified into tensor, vector and scalar types. In a previous paper, tensor perturbations were analyzed. In this paper we study vector and scalar perturbations. We show that vector perturbations can be analyzed in general using an S-deformation approach and do not introduce instabilities. On the other hand, we show by analyzing an explicit example that, contrary to what happens in Einstein gravity, scalar perturbations may lead to instabilities in black holes with spherical horizons when the Gauss-Bonnet string corrections are taken into account.