Appears in collection : Korea-France Joint Workshop on String Theory

In this talk, I will describe the scattering of gravitational waves from compact objects in worldline effective field theory. The Feynman-diagram expansion can be reorganized as the Born series of an effective wave equation, with distinct contributions from long-distance gravitational interactions and short-distance tidal effects. I will explain how the resulting partial-wave amplitudes can be summed to obtain the momentum-space gravitational Compton amplitude, revealing an underlying elliptic function space. Our results through $\mathcal{O}(G^7)$ show the contributions of static, dynamical, and dissipative Love numbers, and the first ultraviolet divergence which requires finite-size worldline operators as counterterms. Finally, I will discuss matching to black-hole perturbation theory and the on-shell vanishing of static Schwarzschild Love numbers.