Radiative contribution to classical gravitational scattering at the third order in $G$

TL;DR

The study analyzes classical gravitational scattering in the post-Minkowskian framework and demonstrates that radiation-reaction from gravitational-wave emission contributes an $O(G^3)$ correction to the conservative scattering angle, canceling the high-energy logarithmic divergence and yielding a finite high-energy limit. The authors compute the radiated angular momentum at $O(G^2)$ from the waveform memory, relate it to the scattering angle, and integrate this with the known conservative 3PM result to obtain a radiation-corrected total 3PM angle. The finite high-energy limit of the total angle precisely matches the massless, two-loop ACV eikonal result, establishing a deep link between classical radiation effects and quantum eikonal predictions. The work clarifies the role of radiation in PM gravity, addresses longstanding puzzles about the 3PM dynamics, and outlines a roadmap for extending the approach to higher orders and potential formulations.

Abstract

Working within the post-Minkowskian approach to General Relativity, we prove that the radiation-reaction to the emission of gravitational waves during the large-impact-parameter scattering of two (classical) point masses modifies the conservative scattering angle by an additional contribution of order $G^3$ which involves a high-energy (or massless) logarithmic divergence of opposite sign to the one contained in the third-post-Minkowskian result of Bern et al. [Phys. Rev. Lett. {\bf 122}, 201603 (2019)]. The high-energy limit of the resulting radiation-reaction-corrected (classical) scattering angle is finite, and is found to agree with the one following from the (quantum) eikonal-phase result of Amati, Ciafaloni and Veneziano [ Nucl. Phys. B {\bf 347}, 550 (1990)].