Instability of spherically symmetric black holes in quadratic gravity

Abstract

We investigate the linear stability of the two known branches of spherically symmetric black holes in quadratic gravity. We extend previous work on the long-wavelength (Gregory-Laflamme) instability of the Schwarzschild branch to a corresponding long-wavelength instability in the non-Schwarzschild branch. In both cases, the instability sets in below a critical horizon radius at which the two black-hole branches intersect. This suggests that classical perturbations enforce a lower bound on the horizon radius of spherically symmetric black holes in quadratic gravity.