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

• Received 18 June 2013

DOI:https://doi.org/10.1103/PhysRevD.88.024039