Angular Momentum Loss Due to Spin-Orbit Effects in the Post-Minkowskian Expansion

We calculate the spin-orbit corrections to the loss of angular momentum in a two-body scattering at third Post-Minkowskian order, $\mathcal O(G^3)$, from scattering amplitudes using the eikonal operator. These results include effects linear in spin, are valid for generic spin orientations and are presented in a manifestly Poincar\'e covariant way. We include both radiative losses, by means of the leading-order gravitational waveform, and static losses by means of the appropriate $-i0$ prescription in the leading soft graviton theorem, finding agreement with known results in the Post-Newtonian limit.