Stability of Lovelock Black Holes under Tensor Perturbations

Abstract

We study the stability of static black holes in the third order Lovelock theory. We derive a master equation for tensor perturbations. Using the master equation, we analyze the stability of Lovelock black holes mainly in seven and eight dimensions. We find there are cases where the linear analysis breaks down. If we restrict ourselves to the regime where the linear analysis is legitimate, black holes are always stable in seven dimensions. However, in eight dimensions, there exists a critical mass below which black holes are unstable. Combining our result in the third order Lovelock theory with the previous one in Einstein-Gauss-Bonnet theory, we conjecture that small black holes are unstable in any dimensions. The instability found in this paper will be important for the analysis of black holes at the LHC.

22 pages, 7 figures;v3:references added

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• A cautionary case of casual causality
• A simple test for stability of black hole by $S$-deformation
• Testing the Weak Cosmic Censorship Conjecture in Lanczos-Lovelock gravity
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• The (in)stability of quasinormal modes of Boulware-Deser-Wheeler black hole in the hyperboloidal framework
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• Tensorial perturbations and stability of spherically symmetric d-dimensional black holes in string theory
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