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

Stability of Schwarzschild black holes in fourth-order gravity revisited