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Communications in Mathematical Physics

, Volume 65, Issue 1, pp 45–76 | Cite as

On the proof of the positive mass conjecture in general relativity

  • Richard Schoen
  • Shing-Tung Yau
Article

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.

Keywords

Neural Network General Relativity Complex System Nonlinear Dynamics Total Mass 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Richard Schoen
  • Shing-Tung Yau

There are no affiliations available

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