Gravitational instability of Einstein-Gauss-Bonnet black holes under tensor mode perturbations

We analyse the tensor mode perturbations of static, spherically symmetric solutions of the Einstein equations with a quadratic Gauss-Bonnet term in dimension D > 4. We show that the evolution equations for this type of perturbation can be cast in a Regge-Wheeler-Zerilli form, and obtain the exact potential for the corresponding Schrodinger-like stability equation. As an immediate application we prove that for D not equal 6 and a > 0, the sign choice for the Gauss-Bonnet coefficient suggested by string theory, all positive mass black holes of this type are stable. In the exceptional case D = 6, we find a range of parameters where positive mass asymptotically flat black holes, with regular horizon, are unstable. This feature is found also in general for a < 0.