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

Differential Geometry Mathematical Physics mathscidoc:2105.10001

Communication in Mathematical Physics, 2021.4
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 \`a 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.
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@inproceedings{po-ning2021evolution,
  title={Evolution of angular momentum and center of mass at null infinity},
  author={Po-Ning Chen, Jordan Keller, Mu-Tao Wang, Ye-Kai Wang, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210507232100111237817},
  booktitle={Communication in Mathematical Physics},
  year={2021},
}
Po-Ning Chen, Jordan Keller, Mu-Tao Wang, Ye-Kai Wang, and Shing-Tung Yau. Evolution of angular momentum and center of mass at null infinity. 2021. In Communication in Mathematical Physics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210507232100111237817.
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