Angular momentum and memory effect

TL;DR

This paper addresses the supertranslation ambiguity in defining angular momentum in general relativity, linking it to gravitational wave memory, and proposes a method to define a supertranslation invariant angular momentum.

Contribution

It introduces a new approach to remove supertranslation ambiguity by accounting for gravitational wave memory, enabling a well-defined angular momentum at null infinity.

Findings

Supertranslation ambiguity is linked to gravitational wave memory.

Proper subtraction of memory yields a supertranslation invariant angular momentum.

The method clarifies angular momentum definition in gravitational systems.

Abstract

It is a long-standing problem in general relativity that the notion of angular momentum of an isolated system has supertranslation ambiguity. In this paper, we argue that the ambiguity is essentially because of the gravitational wave memory. When properly subtracting the memory effect of the observer, one can introduce a supertranslation invariant definition of the angular momentum at null infinity.