Supertranslation invariance of angular momentum at null infinity in double null gauge

TL;DR

This paper demonstrates that the Chen-Wang-Yau angular momentum remains invariant under supertranslations in the double null gauge, extending previous results and clarifying the gauge's supertranslation ambiguity.

Contribution

The authors establish supertranslation invariance of the CWY angular momentum in the double null gauge, resolving ambiguity issues and extending prior work from the Bondi-Sachs formalism.

Findings

CWY angular momentum is supertranslation invariant in double null gauge

Supertranslation ambiguity in the double null gauge is identified and addressed

Invariance also applies to the CWY center of mass integral

Abstract

The supertranslation invariance of the Chen-Wang-Yau (CWY) angular momentum in the Bondi-Sachs formalism/gauge was ascertained by the authors in \cite{CKWWY_evol, CWWY_atmp}. In this article, we study the corresponding problem in the double null gauge. In particular, supertranslation ambiguity of this gauge is identified and the CWY angular momentum is proven to be free of this ambiguity. A similar result is obtained for the CWY center of mass integral.