Instability of spherically-symmetric black holes in Quadratic Gravity

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.