Note on post-Minkowskian expansion and Bondi coordinates

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.