Instability of Schwarzschild–AdS black hole in Einstein–Weyl gravity

We investigate the classical stability of Schwarzschild–AdS black hole in a massive gravity theory of the Einstein–Weyl gravity. It turns out that the linearized Einstein tensor perturbations exhibit unstable modes featuring the Gregory–Laflamme instability of five-dimensional AdS black string, in contrast to the stable Schwarzschild–AdS black hole in Einstein gravity. We point out that the instability of the black hole in the Einstein–Weyl gravity arises from the massiveness but not a feature of fourth-order derivative theory giving ghost states.