Objects in a background gravitational field get tidally deformed, resulting in a response whose conservative part is given by a set of coefficients, commonly referred to as Love numbers. For black holes in four spacetime dimensions, the Love numbers are notoriously zero in the static regime. I will present our work showing this result continues to hold upon inclusion of nonlinearities in the theory for Schwarzschild black holes. We solve the static limit of quadratic Einstein equations on the Schwarzschild background in full generality and show solutions take simple analytic expressions - they are finite polynomials. Matching these results to the point-particle effective field theory we find quadratic Love numbers are zero to all orders in the derivative (multipole) expansion, like the linear ones. I will comment on the relation between this result and near-zone symmetries of black hole perturbations and some possible future directions.
Jacopo Mazza
