Comparison of definitions of angular momentum at null infinity

TL;DR

This paper reviews various definitions of angular momentum at null infinity, highlighting their differences and proposing a new supertranslation-invariant definition under specific conditions.

Contribution

It provides a comprehensive comparison of existing notions and introduces a novel, supertranslation-invariant angular momentum definition at null infinity.

Findings

Identifies key differences among existing angular momentum definitions.

Proposes a new supertranslation-invariant angular momentum concept.

Clarifies the implications of supertranslation ambiguities.

Abstract

The supertranslation ambiguity of angular momentum at null infinity creates a technical difficulty in choosing the proper definition for this conserved quantity. As a result, many different approaches are found in the literature. This article aims to review the most relevant of these notions and compare their most significant properties. A new definition of angular momentum at null infinity is also proposed, which is supertranslation invariant under certain assumptions.