Conserved quantities in general relativity -- the view from null infinity

TL;DR

This paper reviews recent advances in defining conserved quantities like angular momentum and center of mass at null infinity in general relativity, addressing previous ambiguities using new quasilocal approaches.

Contribution

It discusses recent definitions of angular momentum and center of mass at null infinity that resolve supertranslation ambiguities through quasilocal methods.

Findings

New definitions are free of supertranslation ambiguity

Quasilocal conserved quantities are used to define angular momentum and center of mass

Recent developments clarify the understanding of conserved quantities in asymptotically flat spacetimes

Abstract

In general relativity, an idealized distant observer is situated at future null infinity where light rays emitted from the source approach. This article concerns conserved quantities such as mass, energy-momentum, angular momentum, and center of mass at future null infinity. The classical definitions of Bondi mass at future null infinity ascertains the mass radiated away in gravitational waves distinctively. However, the same question for other conserved quantities such as angular momentum has been a subtle issue since the discovery of "supertranslation ambiguity" in the 1960's. Recently, new definitions of angular momentum and center of mass were proposed and proved to be free of such ambiguity [12,14]. These new definitions arise as limits of the Chen-Wang-Yau quasilocal conserved quantities, which are based on the theory of optimal isometric embedding and quasilocal mass of Wang-Yau. It is the purpose of this note to discuss these recent developments