Gravitational waves from coalescing binary systems represent a unique channel to study the fundamental properties of gravity and compact objects in the strong-field regime. As we move toward an era of precision physics with gravitational waves, increasingly accurate waveform templates will be necessary. This requires in particular a precise understanding of the conservative and dissipative dynamics of two-body systems, which includes tidal effects.In gravity theories, the conservative tidal deformability of a self-gravitating object is parametrized in terms of a set of coefficients, commonly referred to as Love numbers, and is derived, at leading order, by solving the linearized static Einstein equations for the perturbations. In the talk, I will discuss the role of field nonlinearities in the calculation of the tidal deformability of compact objects. I will show that the nonlinear Love numbers of black holes are identically zero, a result that extends the well-known vanishing of linear Love numbers to higher orders in perturbation theory. I will show that, remarkably, this is a consequence of a fully nonlinear hidden structure of symmetries in general relativity.
P. Pani