Hidden simplicity in the scattering for neutron stars and black holes

Abstract

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 multi-loop integrands simply by differentiation with respect to the spin. As a first application of the Kerr generating functions, we study 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 $\mathcal{O}(G^5)$ result.

Figures (1)

• Figure 1: Multi-triangle diagram for the scattering of a neutron star in a black hole background. This class of diagrams serves as a generating function for scattering in a Kerr black hole background.