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

TL;DR

This paper studies the stability of Schwarzschild-AdS black holes in Einstein-Weyl gravity, revealing an instability due to massive perturbations, contrasting with their stability in standard Einstein gravity.

Contribution

It demonstrates that Schwarzschild-AdS black holes are unstable under linear perturbations in Einstein-Weyl gravity due to massive modes, unlike in Einstein gravity.

Findings

Unstable modes similar to Gregory-Laflamme instability are found.

Instability arises from the massiveness of perturbations, not ghost states.

Schwarzschild-AdS black holes are stable in Einstein gravity.

Abstract

We investigate the classical stability of Schwarzschild-AdS black hole in a massive 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 the Einstein-Weyl gravity. We confirm 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.