Evaluating small sphere limit of the wangyau quasi-local energy

Po-Ning Chen Mu-Tao Wang Shing-Tung Yau

Mathematical Physics mathscidoc:1912.43642

Communications in Mathematical Physics, 357, (2), 731-774, 2018.1
In this article, we study the small sphere limit of the WangYau quasi-local energy defined in Wang and Yau (Phys Rev Lett 102(2):021101, 2009, Commun Math Phys 288(3):919942, 2009). Given a point <i>p</i> in a spacetime <i>N</i>, we consider a canonical family of surfaces approaching <i>p</i> along its future null cone and evaluate the limit of the WangYau quasi-local energy. The evaluation relies on solving an optimal embedding equation whose solutions represent critical points of the quasi-local energy. For a spacetime with matter fields, the scenario is similar to that of the large sphere limit found in Chen etal. (Commun Math Phys 308(3):845863, 2011). Namely, there is a natural solution which is a local minimum, and the limit of its quasi-local energy recovers the stress-energy tensor at <i>p</i>. For a vacuum spacetime, the quasi-local energy vanishes to higher order and the solution of the optimal embedding
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@inproceedings{po-ning2018evaluating,
  title={Evaluating small sphere limit of the wangyau quasi-local energy},
  author={Po-Ning Chen, Mu-Tao Wang, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204658620752206},
  booktitle={Communications in Mathematical Physics},
  volume={357},
  number={2},
  pages={731-774},
  year={2018},
}
Po-Ning Chen, Mu-Tao Wang, and Shing-Tung Yau. Evaluating small sphere limit of the wangyau quasi-local energy. 2018. Vol. 357. In Communications in Mathematical Physics. pp.731-774. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204658620752206.
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