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A New Quasi-local Mass and Positivity

Xiao Zhang
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Abstract

We use an idea of Wang and Yau to give a new definition of quasi-local mass for a topological sphere in an initial date set. The new definition modifies Brown-York's definition by using certain spinor norm as lapse function. And it requires mean curvature of the topological sphere satisfies apparent horizon conditions, the topological sphere can be isometrically into Euclidean 3-space and mean curvature of the initial date set does not change sign. The positivity holds if we further assume the image of the topological sphere in Euclidean 3-space has nonnegative mean curvature.

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Xiao Zhang. 2007-11-21. A New Quasi-local Mass and Positivity. https://arxiv.org/abs/gr-qc/0603004

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