Love numbers beyond GR and non-linear scalar tidal deformation

In General Relativity (GR), including Einstein-Maxwell theory, it is remarkable that all asymptotically flat black hole (BH) solutions have vanishing Love numbers. Consequently, the Love numbers of BHs present an excellent opportunity to examine any deviations from GR. We will investigate tidal deformations concerning neutral BHs and extremal BHs in EFT of gravity. In four dimensions, the primary contribution to the tidal Love numbers of neutral BHs arises from six derivative operators, while the Love numbers of extremal BHs are subject to corrections from four derivative operators. These higher-order derivative operators are restricted by causality bounds and the Weak Gravity Conjecture. This implies that the Love numbers of BHs contain meaningful information about the UV theory. Additionally, we will explore the non-linear aspects of scalar Love numbers. Intriguingly, it is discovered that non-linear sigma models possess Love numbers that vanish to all orders in perturbation theory.