Radiative contributions to gravitational scattering

TL;DR

This work develops a purely classical, variation-of-constants framework to compute radiation-reaction contributions to the impulse in gravitational two-body scattering, including CM recoil and relative-motion effects, and extends results through 3PM and 4PM with NNLO PN accuracy for radiative losses. It provides explicit RR impulse formulas, demonstrates mass-polynomiality constraints, and computes the conservative radiation-graviton contribution at 4PM (up to 6PN nonlocal terms), enabling cross-validation with EFT and TF approaches. The authors compare their classical results with quantum-amplitude and EFT results, reporting agreement at 3PM but notable disagreements at higher orders (notably in the 5PN/EFT sector), and discuss the potential role of nonlinear RR effects and Green's-function choices. The paper thus offers a cohesive classical backbone for radiative corrections in gravitational scattering, clarifying the interplay between relative dynamics, recoil, radiated fluxes, and nonlocal effects, and outlining paths for resolving outstanding discrepancies with EFT/TF analyses.

Abstract

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 non-trivial identities relating the various radiative losses. At order $G^3$ our results lead to a streamlined classical derivation of results recently derived within a quantum approach. At order $G^4$ 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 {\it conservative} $O(G^4)$ scattering. At orders $G^5$ and $G^6$ 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. B \textbf{965}, 115352 (2021)] but exhibit some disagreements with results of [Phys. Rev. D \textbf{101}, 064033 (2020)].