Radiative contributions to gravitational scattering

The linear-order effects of radiation-reaction on the classical scattering of two point masses, in general relativity, are derived by a variation-of-constants method. Explicit expressions for the radiation-reaction contributions to the changes of 4-momentum during scattering are given to linear order in the radiative losses of energy, linear-momentum, and angular momentum. The polynomial dependence on the masses of the 4-momentum changes is shown to lead to nontrivial identities relating the various radiative losses. At order G3 our results lead to a streamlined classical derivation of results recently derived within a quantum approach. At order G4 we compute the needed radiative losses to next-to-next-to-leading-order in the post-Newtonian expansion, thereby reaching the absolute fourth and a half post-Newtonian level of accuracy in the 4-momentum changes. We also provide explicit expressions, at the absolute sixth post-Newtonian accuracy, for the radiation-graviton contribution to conservative O(G4) scattering. At orders G5 and G6 we derive explicit theoretical expressions for the last two hitherto undetermined parameters describing the fifth-post-Newtonian dynamics. Our results at the fifth-post-Newtonian level confirm results of [Nucl. Phys. B965, 115352 (2021)NUPBBO0550-321310.1016/j.nuclphysb.2021.115352] but exhibit some disagreements with results of [Phys. Rev. D 101, 064033 (2020)PRVDAQ2470-001010.1103/PhysRevD.101.064033].