Vanishing of Nonlinear Tidal Love Numbers of Schwarzschild Black Holes

Love numbers describe the induced conservative response of an object subject to the action of an external gravitational field. They offer insight into the body's internal structure, and can be used to test gravity in the strong-field regime. In particular, Linear Love numbers are known to be zero for Schwarzschild black holes in four dimensions. In this talk I show how to extend this result to include nonlinear effects. I define these coefficients as Wilson couplings in the context of the point-particle effective field theory (EFT). After finding an explicit solution for the (static) response of a perturbed Schwarzschild black hole, I perform a matching with the aforementioned EFT, showing that: (i) the vanishing of the linear Love numbers is robust against nonlinear corrections and (ii) the quadratic Love number couplings also vanish.