Note on post-Minkowskian expansion and Bondi coordinates

TL;DR

This paper transforms the linear post-Minkowskian metric into Bondi coordinates and demonstrates that the Bondi 4-momentum and angular momentum align with relativistic definitions, avoiding supertranslation ambiguities.

Contribution

It provides a method to express the linear post-Minkowskian metric in Bondi coordinates and confirms the physical consistency of Bondi quantities with relativistic definitions.

Findings

Bondi 4-momentum matches relativistic 4-momentum

Bondi angular momentum aligns with relativistic angular momentum

Angular momentum at null infinity is supertranslation free

Abstract

In this note, we transform the linear order (at order $G$) metric from a system of pointlike bodies source in the post-Minkowskian expansion to the Bondi coordinates. We show that the Bondi 4-momentum and angular momentum coincide with the relativistic definitions of 4-momentum and angular momentum for the system of pointlike bodies. The angular momentum computed at the null infinity is free of supertranslation ambiguity.