Radial fall: the gravitational waveform up to the second-and-half Post-Newtonian order

TL;DR

This paper applies the Multipolar Post Minkowskian formalism to analyze a two-body system in radial fall, computing the gravitational waveform up to 2.5 Post-Newtonian order, including radiation reaction effects.

Contribution

It provides the first detailed 2.5PN order gravitational waveform for radial fall, incorporating radiation reaction and inertial force contributions.

Findings

Computed gravitational waveform up to 2.5PN order.

Evaluated energy, angular momentum, and linear momentum emissions.

Analyzed inertial forces at 4.5PN order.

Abstract

We consider an application of the Multipolar Post Minkowskian formalism to the case of a two-body system in radial fall. We compute, within the post-Newtonian approximation, the associated gravitational waveform reaching the 2.5 Post-Newtonian accuracy level. At this level the presence of a radiation-reaction force manifests, modifying the fall with a corresponding bremsstrahlung radiation. We evaluate then all emissions: energy, angular momentum (vanishing identically) and linear momentum. We also evaluate the (nonlocal) inertial forces contributions appearing (at the next PN order, 4.5PN) in the center-of-mass due to the losses paving the way for future more accurate computations.