Nonlinearities in the tidal Love numbers of black holes

Tidal Love numbers describe the linear response of a compact object under the presence of external tidal perturbations, and they are found to vanish exactly for black holes within General Relativity. In this paper we investigate the tidal deformability of neutral black holes when nonlinearities in the theory are taken into account. As a case in point, we consider scalar tidal perturbations on the black hole background, and find that the tidal Love numbers may be nonvanishing depending on the scalar interactions in the bulk theory. Remarkably, for nonlinear sigma models, we find that the tidal Love numbers vanish to all orders in perturbation theory.