Radiated momentum in gravitational two-body scattering including time-asymmetric effects

We compute to high post-Newtonian accuracy the 4-momentum (linear momentum and energy), radiatedas gravitational waves in a two-body system undergoing gravitational scattering. We include, for the firsttime, all the relevant time-asymmetric effects that arise when consistently going three post-Newtonianorders beyond the leading post-Newtonian order. We find that the inclusion of time-asymmetric radiativeeffects (both in tails and in the radiation-reacted hyperbolic motion) is crucial to ensure the masspolynomiality of the post-Minkowskian expansion (G expansion) of the radiated 4-momentum. Imposingthe mass polynomiality of the corresponding individual impulses determines the conservativelikeradiative contributions at the fourth post-Minkowskian order and strongly constrains them at the fifthpost-Minkowskian order.