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

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 ${\mathrm{\Sigma }}_{\text{k}}^n\times {\mathbb{R}}^{+}$, ${\mathrm{\Sigma }}_{\text{k}}^n$ an $n-$manifold of constant curvature $\text{k}$. 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.