A remark on the rigidity case of the positive energy theorem

Details A remark on the rigidity case of the positive energy theorem A remark on the rigidity case of the positive energy theorem

2010-04-30

arxiv.org/abs/1004.5430v1

Mathematics

Differential Geometry

7 pages

Scientific paper

In their proof of the positive energy theorem, Schoen and Yau showed that every asymptotically flat spacelike hypersurface M of a Lorentzian manifold which is flat along M can be isometrically imbedded with its given second fundamental form into Minkowski spacetime as the graph of a function from R^n to R; in particular, M is diffeomorphic to R^n. In this short note, we give an alternative proof of this fact. The argument generalises to the asymptotically hyperbolic case, works in every dimension n, and does not need a spin structure.

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