Evaluating quasilocal energy and solving optimal embedding equation at null infinity

Po-Ning Chen Columbia University Mu-Tao Wang Columbia University Shing-Tung Yau Harvard University

Differential Geometry mathscidoc:1608.10042

Communications in Mathematical Physics , 308, (3), 845-863, 2011
We study the limit of quasilocal energy defined in [7] and [8] for a family of spacelike 2-surfaces approaching null infinity of an asymptotically flat spacetime. It is shown that Lorentzian symmetry is recovered and an energy-momentum 4-vector is obtained. In particular, the result is consistent with the Bondi–Sachs energy-momentum at a retarded time. The quasilocal mass in [7] and [8] is defined by minimizing quasilocal energy among admissible isometric embeddings and observers. The solvability of the Euler-Lagrange equation for this variational problem is also discussed in both the asymptotically flat and asymptotically null cases. Assuming analyticity, the equation can be solved and the solution is locally minimizing in all orders. In particular, this produces an optimal reference hypersurface in the Minkowski space for the spatial or null exterior region of an asymptotically flat spacetime.
quasilocal energy, optimal embedding equation
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@inproceedings{po-ning2011evaluating,
  title={Evaluating quasilocal energy and solving optimal embedding equation at null infinity},
  author={Po-Ning Chen, Mu-Tao Wang, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160820233022601192346},
  booktitle={Communications in Mathematical Physics },
  volume={308},
  number={3},
  pages={845-863},
  year={2011},
}
Po-Ning Chen, Mu-Tao Wang, and Shing-Tung Yau. Evaluating quasilocal energy and solving optimal embedding equation at null infinity. 2011. Vol. 308. In Communications in Mathematical Physics . pp.845-863. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160820233022601192346.
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