(In)stability ofD-dimensional black holes in Gauss-Bonnet theory

We make an extensive study of evolution of gravitational perturbations of $D$-dimensional black holes in Gauss-Bonnet theory. There is an instability at higher multipoles $\ell$ and large Gauss-Bonnet coupling $\alpha$ for $D=5$, 6, which is stabilized at higher $D$. Although a small negative gap of the effective potential for the scalar type of gravitational perturbations exists for higher $D$ and whatever $\alpha$, it does not lead to any instability.