Equations of motion of compact binaries at the third post-Newtonian order

TL;DR

This paper derives the equations of motion for compact binary systems at the third post-Newtonian order, addressing regularization issues to obtain complete and accurate results for circular orbits.

Contribution

It introduces a combined regularization approach using Hadamard and dimensional regularization to fully determine 3PN equations of motion.

Findings

Complete 3PN equations of motion for circular orbits

Resolution of regularization ambiguity with dimensional regularization

Provides energy expressions at 3PN order

Abstract

The equations of motion of two point masses in harmonic coordinates are derived through the third post-Newtonian (3PN) approximation. The problem of self-field regularization (necessary for removing the divergent self-field of point particles) is dealt with in two separate steps. In a first step the extended Hadamard regularization is applied, resulting in equations of motion which are complete at the 3PN order, except for the occurence of one and only one unknown parameter. In a second step the dimensional regularization (in d dimensions) is used as a powerful argument for fixing the value of this parameter, thereby completing the 3-dimensional Hadamard-regularization result. The complete equations of motion and associated energy at the 3PN order are given in the case of circular orbits.