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

G.DOTTI Y R.J.GLEISER

CLASSICAL AND QUANTUM GRAVITY

IOP PUBLISHING LTD

Año: 2005 vol. 22 p. 1 - 6

0264-9381

We analyze 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 perturbations can be cast in a Regge-Wheeler-Zerilli form, and obtain the exact potential for the corresponding Schr"odinger-like stability equation. As an immediate application we prove that for $D eq 6$ and $alpha >0$, 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 $alpha < 0$.