Hidden simplicity in the scattering for neutron stars and black holes

Heavy particle effective theory applied to spinning black holes provides a natural framework in which propagators linearize and numerators exponentiate. In this work, we exploit these two features to introduce Kerr generating functions, which describe the scattering of any probe on a Kerr black hole background to all loop orders. These generating functions can be used to perform the tensor reduction of multiloop integrands simply by differentiation with respect to the spin. As a first application of the Kerr generating functions, we study the leading nonlinear tidal effects of a neutron star in a Kerr black hole background. We organize the integrand by the helicity configuration of the exchanged gravitons and provide compact all-loop-order results for several helicity sectors and a full four-loop O ( G 5 ) result for the leading nonlinear tidal operators.