Third post-Newtonian gravitational radiation from two-body scattering II. Hereditary Energy radiation

TL;DR

This paper calculates the hereditary part of third post-Newtonian gravitational energy radiation during hyperbolic and parabolic scatterings of non-spinning compact objects, providing detailed expressions up to high orders in angular momentum expansion.

Contribution

It introduces a comprehensive third post-Newtonian calculation of hereditary gravitational radiation for hyperbolic encounters, including exact solutions for parabolic cases and high-order angular momentum terms.

Findings

Derived energy radiation expressions up to 1/j^{15} order.

Provided exact solutions for parabolic scattering cases.

Presented complete third post-Newtonian energy radiation formulas.

Abstract

We compute the hereditary part of the third post-Newtonian accurate gravitational energy radiation from hyperbolic scatterings (and parabolic scatterings) of non-spinning compact objects. We employ large angular momentum ($j$) expansion, and compute it to the relative $1/j^{11}$ order (so the first 12 terms). For parabolic scattering case, the exact solution is computed. At the end, the completely collected expression of the energy radiation upto the third post-Newtonian and from $1/j^{3}$ to $1/j^{15}$ order, is presented including the instantaneous contribution.