Evolution of Angular Momentum and Center of Mass at Null Infinity

Po Ning Chen, Jordan Keller, Mu Tao Wang, Ye Kai Wang, Shing Tung Yau

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We study how conserved quantities such as angular momentum and center of mass evolve with respect to the retarded time at null infinity, which is described in terms of a Bondi–Sachs coordinate system. These evolution formulae complement the classical Bondi mass loss formula for gravitational radiation. They are further expressed in terms of the potentials of the shear and news tensors. The consequences that follow from these formulae are (1) Supertranslation invariance of the fluxes of the CWY conserved quantities. (2) A conservation law of angular momentum à la Christodoulou. (3) A duality paradigm for null infinity. In particular, the supertranslation invariance distinguishes the CWY angular momentum and center of mass from the classical definitions.

Original languageEnglish
Pages (from-to)551-588
Number of pages38
JournalCommunications in Mathematical Physics
Issue number1
Publication statusPublished - 2021 Aug

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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