The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: From Source to Canonical Moment

TL;DR

This paper derives the explicit form of the canonical quadrupole moment for compact binaries at 4PN order, a key step in precise gravitational-wave modeling for binary systems.

Contribution

It provides the first detailed expression of the canonical quadrupole moment at 4PN order, linking source and gauge moments through a non-linear diffeomorphism.

Findings

Explicit 4PN canonical quadrupole moment expression

Constructed non-linear diffeomorphism between moments

Advances gravitational-wave phase modeling at 4PN

Abstract

As a crucial step towards the completion of the fourth post-Newtonian (4PN) gravitational-wave generation from compact binary systems, we obtain the expressions of the so-called "canonical" multipole moments of the source in terms of the "source" and "gauge" moments. The canonical moments describe the propagation of gravitational waves outside the source's near zone, while the source and gauge moments encode explicit information about the matter source. Those two descriptions, in terms of two sets of canonical moments or in terms of six sets of source and gauge moments, are isometric. We thus construct the non-linear diffeomorphism between them up to the third post-Minkowskian order, and we exhibit the concrete expression of the canonical mass-type quadrupole moment at the 4PN order. This computation is one of the last missing pieces for the determination of the gravitational-wave phasing of compact binary systems at 4PN order.