Equations of motion according to the asymptotic post-Newtonian scheme for general relativity

TL;DR

This paper reviews the asymptotic post-Newtonian approximation in general relativity, focusing on equations of motion for mass centers and analyzing the emergence of a new term in these equations.

Contribution

It provides a detailed summary of the asymptotic post-Newtonian scheme and introduces a new term in the equations of motion for mass centers.

Findings

Derivation of equations for mass center motion in the PN scheme

Identification of a new term in the equations of motion

Discussion on the implications of the new term

Abstract

We summarize a recent work done on the title's subject. First, we present the asymptotic scheme of post-Newtonian (PN) approximation for general relativity in the harmonic gauge. Then, we discuss the definition of the mass centers and the derivation of equations for their motion, following that scheme. Finally, we briefly analyze the reason why a new term has thus been found in the equations of motion.