New derivation of a third post-Newtonian equation of motion for relativistic compact binaries without ambiguity

TL;DR

This paper derives a clear, unambiguous third post-Newtonian equation of motion for relativistic binary stars, improving precision in modeling their inspiral dynamics without ambiguity.

Contribution

The paper presents a novel derivation of the 3 PN equation of motion for compact binaries without ambiguity, using harmonic coordinates and strong field point particle limit.

Findings

Explicit 3 PN equations of motion provided

Energy expressions for circular orbits derived

Equation is Lorentz invariant and conserved

Abstract

A third post-Newtonian (3 PN) equation of motion for an inspiralling binary consisting of two spherical compact stars with strong internal gravity is derived under harmonic coordinate condition using the strong field point particle limit. The equation of motion is complete in a sense that it is Lorentz invariant in the post-Newtonian perturbative sense, admits conserved energy of the orbital motion, and is unambiguous, that is, with no undetermined coefficient. In this paper, we show explicit expressions of the 3 PN equation of motion and an energy of the binary orbital motion in case of the circular orbit (neglecting the 2.5 PN radiation reaction effect) and in the center of the mass frame. It is argued that the 3 PN equation of motion we obtained is physically unambiguous. Full details will be reported elsewhere.