Radiative contributions to gravitational scattering

TL;DR

This paper derives linear-order radiation-reaction effects on gravitational scattering of point masses in General Relativity, providing explicit expressions up to high post-Newtonian orders and clarifying theoretical parameters at fifth order.

Contribution

It offers a detailed classical derivation of radiation-reaction effects, extending calculations to the fourth and sixth post-Newtonian orders and resolving parameters at fifth order.

Findings

Derived explicit radiation-reaction contributions to 4-momentum changes.

Computed radiative losses at next-to-next-to-leading order in post-Newtonian expansion.

Provided explicit expressions for conservative scattering at sixth post-Newtonian accuracy.

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)].