Head-on infall of two compact objects: Third post-Newtonian Energy Flux

TL;DR

This paper derives third post-Newtonian order analytical expressions for gravitational energy flux during head-on infall of two compact objects, including hereditary effects, aiding comparison with numerical relativity.

Contribution

It provides the first detailed third post-Newtonian energy flux calculations for head-on infall, incorporating hereditary contributions such as tails and tail-squared terms.

Findings

Analytical expressions for energy flux from infinity and finite distance infall.

Inclusion of hereditary tail effects at third post-Newtonian order.

Results facilitate comparison with numerical relativity simulations.

Abstract

Head-on infall of two compact objects with arbitrary mass ratio is investigated using the multipolar post-Minkowskian approximation method. At the third post-Newtonian order the energy flux, in addition to the instantaneous contributions, also includes hereditary contributions consisting of the gravitational-wave tails, tails-of-tails and the tail-squared terms. The results are given both for infall from infinity and also for infall from a finite distance. These analytical expressions should be useful for the comparison with the high accuracy numerical relativity results within the limit in which post-Newtonian approximations are valid.