We compute the radiation reacted momentum impulse Δ𝑝𝜇𝑖, spin kick Δ𝑆𝜇𝑖, and scattering angle 𝜃 between two scattered spinning massive bodies (black holes or neutron stars) using the 𝒩 =1 supersymmetric worldline quantum field theory formalism up to fourth post-Minkowskian (4PM) order. Our calculation confirms the state-of-the-art nonspinning results, and extends them to include spin-orbit effects. Advanced multiloop Feynman integral technology including differential equations and the method of regions are applied and extended to deal with the retarded propagators arising in a causal description of the scattering dynamics. From these results we determine a complete set of radiative fluxes at subleading PM order: the 4PM radiated four-momentum and, via linear response, the 3PM radiated angular momentum, both again including spin-orbit effects.
Jakobsen et al. (Tue,) studied this question.