Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order in harmonic coordinates

TL;DR

This paper derives the gravitational radiation-reaction force at the 4.5PN order in harmonic coordinates for compact binary systems, ensuring consistency with known fluxes and Lorentz invariance, aiding comparisons with other methods.

Contribution

It provides the first derivation of the RR force at 4.5PN order in harmonic coordinates using dimensional regularization, confirming known fluxes and Lorentz invariance.

Findings

Derived the 4.5PN RR force in harmonic coordinates.

Confirmed the RR acceleration matches known fluxes.

Verified Lorentz invariance of the RR acceleration.

Abstract

We derive the gravitational radiation-reaction (RR) force in the harmonic coordinate system at the fourth-and-a-half post-Newtonian (4.5PN) order in the case of compact binary systems. Dimensional regularization is used to treat the ultra-violet divergences which appear at that order. We prove that the RR acceleration implies the known radiation fluxes at infinity associated with energy, angular momentum, linear momentum, and center-of-mass position. As a consistency check, we verify the manifest Lorentz invariance of the RR acceleration in harmonic coordinates. Our result should be useful for comparisons with other approaches such as the gravitational self force (GSF) and the post-Minkowskian (PM) effective field theory.