Equation of motion for relativistic compact binaries with the strong field point particle limit : the second and half post-Newtonian order

TL;DR

This paper derives the 2.5 post-Newtonian order equation of motion for relativistic compact binaries with strong internal gravity using a novel strong field point particle limit, confirming its applicability.

Contribution

It introduces a new method to incorporate strong internal gravity into the post-Newtonian framework without delta functions, deriving an accurate equation of motion for compact binaries.

Findings

Derived the 2.5 PN order equation of motion for strong-field binaries

Confirmed agreement with Damour and Deruelle's established equation

Validated the strong field point particle limit approach

Abstract

We study the equation of motion appropriate to an inspiralling binary star system whose constituent stars have strong internal gravity. We use the post-Newtonian approximation with the strong field point particle limit by which we can introduce into general relativity a notion of a point-like particle with strong internal gravity without using Dirac delta distribution. Besides this limit, to deal with strong internal gravity we express the equation of motion in surface integral forms and calculate these integrals explicitly. As a result we obtain the equation of motion for a binary of compact bodies accurate through the second and half post-Newtonian (2.5 PN) order. This equation is derived in the harmonic coordinate. Our resulting equation perfectly agrees with Damour and Deruelle 2.5 PN equation of motion. Hence it is found that the 2.5 PN equation of motion is applicable to a relativistic compact binary.