On the structure of the post-Newtonian expansion in general relativity

TL;DR

This paper presents a new expression for the post-Newtonian metric in general relativity, offering insights into its structure and the gravitational radiation reaction terms, with implications for understanding gravitational fields of isolated systems.

Contribution

It introduces a novel form of the post-Newtonian metric that clarifies the structure of the expansion and the role of radiation reaction effects.

Findings

New expression for the post-Newtonian metric in harmonic coordinates

Insights into the structure of the post-Newtonian expansion

Clarification of gravitational radiation reaction terms

Abstract

In the continuation of a preceding work, we derive a new expression for the metric in the near zone of an isolated matter system in post-Newtonian approximations of general relativity. The post-Newtonian metric, a solution of the field equations in harmonic coordinates, is formally valid up to any order, and is cast in the form of a particular solution of the wave equation, plus a specific homogeneous solution which ensures the asymptotic matching to the multipolar expansion of the gravitational field in the exterior of the system. The new form provides some insights on the structure of the post-Newtonian expansion in general relativity and the gravitational radiation reaction terms therein.