(In)stability of D-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 multi-poles $\ell$ and large Gauss-Bonnet coupling $\alpha$ for $D= 5, 6$, which is stabilized at higher $D$. Although small negative gap of the effective potential for scalar type of gravitational perturbations, exists for higher $D$ and whatever $\alpha$, it does not lead to any instability.