Alternative method for matching post-Newtonian expansion to post-Minkowskian field

TL;DR

This paper introduces an alternative method for matching post-Newtonian and post-Minkowskian solutions in general relativity, providing detailed proofs and expanding on prior matching techniques.

Contribution

It presents a new approach to match post-Newtonian and post-Minkowskian fields, complementing previous methods and offering detailed proofs of key properties.

Findings

Successful development of an alternative matching method

Verification of properties through detailed proofs

Enhanced understanding of post-Newtonian and post-Minkowskian correspondence

Abstract

In 2002, Poujade and Blanchet succeeded in matching the post-Newtonian solution to the Einstein field equation to the post-Minkowskian field up to any arbitrary order as well as reproducing, in a different way, the results of the 1998 paper by Blanchet in which he showed how to match the post-Minkowskian series to the post-Newtonian expansion. Comparing these two papers, it might be asked whether it is possible to match the post-Newtonian field to the post-Minkowskian one by means of a method similar to the one used in the 1998 paper. The answer is affirmative, and in the present paper we provide this alternative method. Furthermore, detailed proofs of several properties and results stated in previous papers are given.