Ambiguity-Free Completion of the Equations of Motion of Compact Binary Systems at the Fourth Post-Newtonian Order

TL;DR

This paper derives the complete equations of motion for two non-spinning compact objects at the 4PN order without ambiguities, using dimensional regularization and matching techniques to resolve previous uncertainties.

Contribution

It provides the first ambiguity-free derivation of 4PN equations of motion for compact binaries, including a first-principles determination of the last ambiguity parameter.

Findings

Ambiguity-free 4PN equations of motion derived

Use of dimensional regularization for IR and UV divergences

Matching between near and far zone fields to fix parameters

Abstract

We present the first complete (i.e., ambiguity-free) derivation of the equations of motion of two non-spinning compact objects up to the 4PN order, based on the Fokker action of point particles in harmonic coordinates. The last ambiguity parameter is determined from first principle, by resorting to a matching between the near zone and far zone fields, and a consistent computation of the 4PN tail effect in d dimensions. Dimensional regularization is used throughout for treating IR divergences appearing at 4PN order, as well as UV divergences due to the model of point particles describing compact objects.