Stability of Schwarzschild black holes in fourth-order gravity revisited

Understand

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 $\alpha=-\beta/3$.