On the equation of motion of compact binaries in Post-Newtonian approximation

TL;DR

This paper derives a third post-Newtonian equation of motion for compact binary stars in harmonic coordinates, ensuring Lorentz invariance, unambiguity, and energy conservation within general relativity.

Contribution

It introduces a novel derivation of the 3 PN equation of motion using the surface integral approach and the strong field point particle limit, incorporating self-gravitating stars.

Findings

The 3 PN equation is Lorentz invariant.

The equation conserves the binary's orbital energy.

The derivation is unambiguous and consistent with general relativity.

Abstract

A third post-Newtonian (3 PN) equation of motion for two spherical compact stars in a harmonic coordinate has been derived based on the surface integral approach and the strong field point particle limit. The strong field point particle limit enables us to incorporate a notion of a self-gravitating regular star into general relativity. The resulting 3 PN equation of motion is Lorentz invariant, unambiguous, and conserves an energy of the binary orbital motion.