On the proof of the positive mass conjecture in general relativity

Richard Schoen Shing-Tung Yau

Mathematical Physics mathscidoc:1912.43463

Communications in Mathematical Physics, 65, (1), 45-76, 1979.2
Let<i>M</i> be a space-time whose local mass density is non-negative everywhere. Then we prove that the total mass of<i>M</i> as viewed from spatial infinity (the ADM mass) must be positive unless<i>M</i> is the flat Minkowski space-time. (So far we are making the reasonable assumption of the existence of a maximal spacelike hypersurface. We will treat this topic separately.) We can generalize our result to admit wormholes in the initial-data set. In fact, we show that the total mass associated with each asymptotic regime is non-negative with equality only if the space-time is flat.
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  title={On the proof of the positive mass conjecture in general relativity},
  author={Richard Schoen, and Shing-Tung Yau},
  booktitle={Communications in Mathematical Physics},
Richard Schoen, and Shing-Tung Yau. On the proof of the positive mass conjecture in general relativity. 1979. Vol. 65. In Communications in Mathematical Physics. pp.45-76. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203419382549027.
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