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

Gustavo Dotti·Reinaldo J. Gleiser
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Abstract

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 $D \neq 6$ and $α>0$, 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 $α< 0$.

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Gustavo Dotti, Reinaldo J. Gleiser. 2004-09-29. Gravitational instability of Einstein-Gauss-Bonnet black holes under tensor mode perturbations. https://doi.org/10.1088/0264-9381%2F22%2F1%2Fl01

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