Rigidity and minimizing properties of quasi-local mass

Po-Ning Chen Columbia University Mu-Tao Wang Columbia University

Mathematical Physics mathscidoc:1608.22007

In this article, we survey recent developments in defining the quasi-local mass in general relativity. We discuss various approaches and the properties and applications of the different definitions. Among the expected properties, we focus on the rigidity property: for a surface in the Minkowski spacetime, one expects that the mass should vanish. We describe the Wang-Yau quasi-local mass whose definition is motivated by this rigidity property and by the Hamilton-Jacobi analysis of the Einstein-Hilbert action. In addition, we survey recent results on the minimizing property the Wang-Yau quasi-local mass.
quasi-local mass, Hamilton-Jacobi analysis, Einstein-Hilbert action, Wang-Yau quasi-local mass
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  title={Rigidity and minimizing properties of quasi-local mass},
  author={Po-Ning Chen, and Mu-Tao Wang},
Po-Ning Chen, and Mu-Tao Wang. Rigidity and minimizing properties of quasi-local mass. 2014. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160820102251502460312.
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