Rigidity and minimizing properties of quasi-local mass
arXiv:1411.6251
Abstract
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.
arXiv comment11 pages
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- Smoothing the Bartnik boundary conditions and other results on Bartnik's quasi-local mass
- Wang and Yau's Quasi-Local Energy for an Extreme Kerr Spacetime
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