Linear stability of Einstein-Gauss-Bonnet static spacetimes. Part I: tensor perturbations

TL;DR

This paper investigates the linear stability of certain static Einstein-Gauss-Bonnet spacetimes under tensor perturbations, providing insights into their robustness in higher-dimensional gravity theories.

Contribution

It offers a detailed analysis of tensor perturbations' stability for a class of static solutions in Einstein-Gauss-Bonnet gravity, focusing on higher-dimensional spacetimes.

Findings

Tensor perturbations' stability conditions derived.

Identification of parameter regimes ensuring stability.

Extension of stability analysis to higher-dimensional static solutions.

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. The analysis in this paper is restricted to tensor perturbations.