Some Remarks on Wang-Yau Quasi-Local Mass

Bowen Zhao, Lars Andersson, Shing-Tung Yau
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Abstract

We review Wang-Yau quasi-local definitions along the line of gravitational Hamiltonian. This makes clear the connection and difference between Wang-Yau definition and Brown-York or even global ADM definition. We make a brief comment on admissibility condition in Wang-Yau quasi-lcoal mass. We extend the positivity proof for Wang-Yau quasi-local energy to allow possible presence of strictly stable apparent horizons through establishing solvability of Dirac equation in certain 3-manifolds that possess cylindrical ends, as in the case of Jang's graph blowing up at marginally outer trapped surfaces.
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关于王友准局域质量的一些评论
我们沿着引力哈密顿的思路回顾了王-尤准局域定义。这明确了王-尤定义与布朗-约克甚至全局 ADM 定义之间的联系与区别。我们简要评述了王尤准局部质量的可接受性条件。我们扩展了旺-尤准局域能的正向证明,通过建立某些具有圆柱末端的三芒星中狄拉克方程的可解性,允许可能存在严格稳定的表观水平面,如张氏图在边缘外困面炸开的情形。
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