Pure and Applied Mathematics Quarterly

Volume 20 (2024)

Number 4

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

Pages: 1635 – 1666

DOI: https://dx.doi.org/10.4310/PAMQ.2024.v20.n4.a5

Authors

Po-Ning Chen (Department of Mathematics, University of California Riverside, Riverside, CA, USA)

Mu-Tao Wang (Department of Mathematics, Columbia University, New York, NY, USA)

Ye-Kai Wang (Department of Applied Mathematics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan)

Shing-Tung Yau (Department of Mathematics, Tsinghua University, Beijing, China)

Abstract

The supertranslation invariance of the Chen-Wang-Yau (CWY) angular momentum in the Bondi-Sachs formalism/gauge was ascertained by the authors in [$\href{https://doi.org/10.1007/s00220-021-04053-7}{12}$, $\href{https://dx.doi.org/10.4310/ATMP.2021.v25.n3.a4}{13}$]. 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.

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Received 28 February 2022

Received revised 25 January 2023

Accepted 13 April 2023

Published 18 July 2024