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We make an extensive study of evolution of gravitational perturbations of D-dimensional black holes in Gauss-Bonnet theory. There is an instability at higher multipoles and large Gauss-Bonnet coupling for D=5, 6, which is stabilized at higher D. Although a small negative gap of the effective potential for the scalar type of gravitational perturbations exists for higher D and whatever, it does not lead to any instability.
Konoplya et al. (Tue,) studied this question.
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