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Volume comparison for hypersurfaces in Lorentzian manifolds and singularity theorems

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Treude, Jan-Hendrik ; Grant, James D. E.
Date of publication of this fulltext: 19 Mar 2012 07:35


We develop area and volume comparison theorems for the evolution of spacelike, acausal, causally complete hypersurfaces in Lorentzian manifolds, where one has a lower bound on the Ricci tensor along timelike curves, and an upper bound on the mean curvature of the hypersurface. Using these results, we give a new proof of Hawking's singularity theorem.

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