Third post-Newtonian gravitational waveforms for compact binary systems in general orbits: Instantaneous terms

TL;DR

This paper calculates the instantaneous third post-Newtonian order gravitational waveforms for compact binaries in general and quasi-elliptical orbits, aiding the development of precise gravitational wave detection templates.

Contribution

It extends previous waveform models by including instantaneous terms up to 3PN order for general and quasi-elliptical orbits, using multipolar post-Minkowskian formalism.

Findings

Computed 3PN instantaneous gravitational wave modes for general orbits.

Extended results to quasi-elliptical orbits using 3PN quasi-Keplerian representation.

Provided basis for more accurate gravitational wave templates.

Abstract

We compute the instantaneous contributions to the spherical harmonic modes of gravitational waveforms from compact binary systems in general orbits up to the third post-Newtonian order. We further extend these results for compact binaries in quasi-elliptical orbits using the 3PN quasi-Keplerian representation of the conserved dynamics of compact binaries in eccentric orbits. Using the multipolar post-Minkowskian formalism, starting from the different mass and current type multipole moments, we compute the spin weighted spherical harmonic decomposition of the instantaneous part of the gravitational waveform. These are terms which are functions of the retarded time and do not depend on the history of the binary evolution. Together with the hereditary part, which depends on the binary's dynamical history, these waveforms form the basis for construction of accurate templates for the detection of gravitational wave signals from binaries moving in quasi-elliptical orbits.