Hidden simplicity in black holes dynamics

Heavy particle effective theory applied to spinning black holes provides a natural framework in which propagators linearize and numerators exponentiate. In this talk, I will 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 multi-loop integrands simply by differentiation with respect to the spin. As a first application of the Kerr generating functions, consider a neutron star in a Kerr black hole background. The integrand is organized by the helicity configuration of the exchanged gravitons. With the use of the Kerr generating functions, compact all-loop-order results for several helicity sectors and a full four-loop result are obtained.