Classical scattering from heavy spinning amplitudes

A recent burst in gravitational wave astronomy has motivated a new perspective on the classical two-body problem by on-shell methods rooted in quantum field theory. Using these methods and the heavy-mass limit, we derive the relevant amplitudes for the scattering of spinning black holes at the first post-Minkowskian (PM) order. In order to push this scattering to the second PM order, we derive  Compton amplitudes free from unphysical poles in the classical limit. The cured amplitudes are subject to deformations by contact terms, the vast majority of whose contributions we can fix by imposing a relation between spin structures motivated by lower spin multipoles of black hole scattering. This gravitational Compton amplitude allows us to push the 2PM scattering to any order in the spin vectors of both objects. We present a closed-form, all-spin expression of the 2PM amplitude between a spinning body and a non-spinning black hole.