Energy-momentum surface density and quasilocal mass in general relativity

Mu-Tao Wang Shing-Tung Yau

Mathematical Physics mathscidoc:1912.43705

arXiv preprint arXiv:0804.1174, 2008.4
We define new energy momentum surface density and quasilocal mass for the boundary surface of a spacelike region in spacetime. Isometric embeddings of such a surface into the Minkowski space are used as reference surfaces in the definition. When the reference surface lies in a flat three-dimensional space slice of the Minkowski space, our expression recovers the Brown-York and Liu-Yau quasilocal mass. Moreover, we prove the positivity of the new quasilocal mass under the dominant energy condition and show that it is zero for surfaces in the Minkowski space.
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@inproceedings{mu-tao2008energy-momentum,
  title={Energy-momentum surface density and quasilocal mass in general relativity},
  author={Mu-Tao Wang, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205118156032269},
  booktitle={arXiv preprint arXiv:0804.1174},
  year={2008},
}
Mu-Tao Wang, and Shing-Tung Yau. Energy-momentum surface density and quasilocal mass in general relativity. 2008. In arXiv preprint arXiv:0804.1174. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205118156032269.
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