The third post-Newtonian gravitational wave polarisations and associated spherical harmonic modes for inspiralling compact binaries in quasi-circular orbits

TL;DR

This paper computes the gravitational waveform for inspiralling compact binaries at the third post-Newtonian order, providing detailed polarization modes and spherical harmonic decomposition to improve gravitational wave data analysis and waveform modeling.

Contribution

It extends the gravitational waveform calculation to 3PN order, including polarization modes and spherical harmonic modes, based on the multipolar post-Minkowskian formalism.

Findings

Provides 3PN accurate gravitational wave templates.

Derives spin-weighted spherical harmonic modes at 3PN order.

Includes hereditary effects like tails and memory at 3PN.

Abstract

The gravitational waveform (GWF) generated by inspiralling compact binaries moving in quasi-circular orbits is computed at the third post-Newtonian (3PN) approximation to general relativity. Our motivation is two-fold: (i) To provide accurate templates for the data analysis of gravitational wave inspiral signals in laser interferometric detectors; (ii) To provide the associated spin-weighted spherical harmonic decomposition to facilitate comparison and match of the high post-Newtonian prediction for the inspiral waveform to the numerically-generated waveforms for the merger and ringdown. This extension of the GWF by half a PN order (with respect to previous work at 2.5PN order) is based on the algorithm of the multipolar post-Minkowskian formalism, and mandates the computation of the relations between the radiative, canonical and source multipole moments for general sources at 3PN order. We also obtain the 3PN extension of the source multipole moments in the case of compact binaries, and compute the contributions of hereditary terms (tails, tails-of-tails and memory integrals) up to 3PN order. The end results are given for both the complete plus and cross polarizations and the separate spin-weighted spherical harmonic modes.