Gravitational quasinormal modes of black holes in quadratic gravity

We study the gravitational perturbations of black holes in quadratic gravity, in which the Einstein-Hilbert term is supplemented by quadratic terms in the curvature tensor. In this class of theories, the Schwarzschild solution can coexist with modified black hole solutions, and both families are radially stable in a wide region of the parameter space. Here we study nonradial perturbations of both families of static, spherically symmetric black holes, computing the quasinormal modes with axial parity and finding strong numerical evidence for the stability of these solutions under axial perturbations. The perturbation equations describe the propagation of a massless and a massive spin-two fields. We show that the Schwarzschild solution admits the same quasinormal modes as in general relativity, together with new classes of modes corresponding to the massive spin-two degrees of freedom. The spectrum of the modified black hole solution has the same structure, but all modes are different from those of general relativity. We argue that both classes of modes can be excited in physical processes, suggesting that a characteristic signature of this theory is the presence of massive spin-two modes in the gravitational ringdown, even when the stationary solution is the same as in general relativity.