Stability of Schwarzschild black holes in fourth-order gravity revisited

Abstract

We revisit the classical stability of Schwarzschild black hole in fourth-order theories of gravity. On the contrary of the stability of this black hole, it turns out that the linearized perturbations exhibit unstable modes featuring the Gregory-Laflamme instability of five-dimensional black string. This shows clearly an instability of black hole in fourth-order gravity with $\alpha =-\beta /3$.

10 pages, no figures, version to appear in PRD

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• Critical Gravity in Four Dimensions
• Stability of f(R) black holes
• Graviton and scalar propagations on AdS(4) space in f(R) gravities
• Critical gravity as van Dam-Veltman-Zakharov discontinuity in anti de Sitter space

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