Momentum recoil in the relativistic two-body problem: higher-order tails

TL;DR

This paper calculates higher-order tail contributions to linear momentum flux in relativistic two-body systems, enhancing understanding of recoil effects during gravitational interactions for various orbital configurations.

Contribution

It provides the first detailed computation of tail-of-tail and tail-squared effects on linear momentum flux in nonspinning binaries for hyperbolic and elliptic orbits, expanding previous energy and angular momentum loss analyses.

Findings

Derived explicit formulas for momentum flux in hyperbolic and elliptic orbits.

Performed orbital averages at leading post-Newtonian order.

Results applicable to high-precision modeling of gravitational scattering.

Abstract

In the description of the relativistic two-body interaction, together with the effects of energy and angular momentum losses due to the emission of gravitational radiation, one has to take into account also the loss of linear momentum, which is responsible for the recoil of the center-of-mass of the system. We compute higher-order tail (i.e., tail-of-tail and tail-squared) contributions to the linear momentum flux for a nonspinning binary system either along hyperboliclike or ellipticlike orbits. The corresponding orbital averages are evaluated at their leading post-Newtonian approximation, using harmonic coordinates and working in the Fourier domain. The final expressions are given in a large-eccentricity (or large-angular momentum) expansion along hyperboliclike orbits and in a small-eccentricity expansion along ellipticlike orbits. We thus complete a previous analysis focusing on both energy and angular momentum losses [Phys. Rev. D \textbf{104}, no.10, 104020 (2021)], providing brick-type results which will be useful, e.g., in the high-accurate determination of the radiated impulses of the two bodies undergoing a scattering process.