Third-and-a-half order post-Newtonian equations of motion for relativistic compact binaries using the strong field point particle limit

TL;DR

This paper rederives the 3.5 post-Newtonian equations of motion for relativistic binary stars using a strong field point particle approach, confirming previous results and clarifying energy relations.

Contribution

It introduces a strong field point particle limit for deriving 3.5 PN equations, providing an alternative to delta function models and confirming prior equations of motion.

Findings

Equations of motion agree with previous 3.5 PN results.

Energy of the star relates simply to its mass up to 3.5 PN order.

Method confirms the validity of the strong field point particle approach.

Abstract

We report our rederivation of the equations of motion for relativistic compact binaries through the third-and-a-half post-Newtonian (3.5 PN) order approximation to general relativity using the strong field point particle limit to describe self-gravitating stars instead of the Dirac delta functional. The computation is done in harmonic coordinates. Our equations of motion describe the orbital motion of the binary consisting of spherically symmetric non-rotating stars. The resulting equations of motion fully agree with the 3.5 PN equations of motion derived in the previous works. We also show that the locally defined energy of the star has a simple relation with its mass up to the 3.5 PN order.