(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 and large Gauss-Bonnet coupling α 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 α, it does not lead to any instability.