Explicit solution of the gravitational two-body problem at the second post-Minkowskian order

TL;DR

This paper provides explicit solutions for the two-body gravitational problem at the second post-Minkowskian order, including conservative and radiation-reacted cases, aiding future gravitational wave research.

Contribution

It offers explicit worldline solutions at second post-Minkowskian order and analyzes momentum and angular momentum changes during scattering.

Findings

Explicit worldline solutions at second post-Minkowskian order

Analysis of momentum and angular momentum changes during scattering

Provides high-order post-Newtonian radiation-reaction acceleration values

Abstract

The worldlines (in harmonic coordinates) of two gravitationally interacting massive bodies at the second post-Minkowskian order are described in explicit form. Both the conservative case and the radiation-reacted case are considered. We use our results to check the changes, during scattering, of the individual momenta, as well as of the total angular momentum. High post-Newtonian order values of the $O(G^2)$ radiation-reaction acceleration components are provided for checks of future post-Newtonian computations.