Radiative contribution to classical gravitational scattering at the third order in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>G</mml:mi></mml:math>
Thibault Damour
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. 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 et al. [Nucl. Phys. B347, 550 (1990)].