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We analyze the tensor mode perturbations of static, spherically symmetricsolutions of the Einstein equations with a quadratic Gauss-Bonnet term indimension $D > 4$. We show that the evolution equations for this type ofperturbations can be cast in a Regge-Wheeler-Zerilli form, and obtain the exactpotential for the corresponding Schr\"odinger-like stability equation. As animmediate application we prove that for $D \neq 6$ and $\alpha >0$, the signchoice for the Gauss-Bonnet coefficient suggested by string theory, allpositive mass black holes of this type are stable. In the exceptional case $D=6$, we find a range of parameters where positive mass asymptotically flatblack holes, with regular horizon, are unstable. This feature is found also ingeneral for $\alpha < 0$.Comment: 7 pages, 1 figure, minor corrections, references adde

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