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

Gustavo Dotti, Reinaldo J Gleiser
2004 Classical and quantum gravity  
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 Schrödinger-like stability equation. As an immediate application we prove that for D ≠ 6 and α >0, the sign choice for the Gauss-Bonnet coefficient suggested by string
more » ... heory, 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 α < 0.
doi:10.1088/0264-9381/22/1/l01 fatcat:25k2wdppszb5voqmdgo2kuvg5y