On the proof of the positive mass conjecture in general relativity
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.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- February 1979
- DOI:
- Bibcode:
- 1979CMaPh..65...45S
- Keywords:
-
- Neural Network;
- General Relativity;
- Complex System;
- Nonlinear Dynamics;
- Total Mass