Abstract
LetM be a space-time whose local mass density is non-negative everywhere. Then we prove that the total mass ofM as viewed from spatial infinity (the ADM mass) must be positive unlessM 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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Schoen, R., Yau, ST. On the proof of the positive mass conjecture in general relativity. Commun.Math. Phys. 65, 45–76 (1979). https://doi.org/10.1007/BF01940959
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DOI: https://doi.org/10.1007/BF01940959