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arXiv · 0706.1166

The Liu-Yau mass as a good quasi-local energy in general relativity

Niall O Murchadha
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Abstract

A quasi-local mass has been a long sought after quantity in general relativity. A recent candidate has been the Liu-Yau mass. One can show that the Liu-Yau mass of any two-surface is the maximum of the Brown-York energy for that two-surface. This means that it has significant disadvantages as a mass. It is much better interpreted as an energy and I will show one way of doing so. The Liu-Yau mass is especially interesting in spherical geometries, where mass and energy are indistinguishable. For a spherical two-surface, it equals the minimum of the amount of energy at rest that one needs to put inside the two-surface to generate the given surface geometry. Thus it gives interesting information about the interior, something no other mass or energy function does.

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Niall O Murchadha. 2007-06-08. The Liu-Yau mass as a good quasi-local energy in general relativity. https://arxiv.org/abs/0706.1166

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