On the angular momentum of compact binary coalescence

TL;DR

This paper discusses the supertranslation ambiguity in defining angular momentum in general relativity and shows that a recent supertranslation-invariant definition aligns with the classical one at the quadrupole level in binary coalescence.

Contribution

It demonstrates that the new supertranslation-invariant angular momentum coincides with the classical definition at the quadrupole level in compact binary coalescence.

Findings

The new angular momentum definition is supertranslation invariant.

It matches the classical angular momentum at the quadrupole level.

Supertranslation ambiguity is often ignored in the binary coalescence community.

Abstract

The supertranslation ambiguity issue of angular momentum is a long-standing problem in general relativity. Recently, there appeared the first definition of angular momentum at null infinity that is supertranslation invariant. However, in the compact binary coalescence community, supertranslation ambiguity is often ignored. This paper demonstrates that we have the happy circumstance that the newly defined angular momentum coincides with the classical definition at the quadrupole level.