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Volume comparison for hypersurfaces in Lorentzian manifolds and singularity theorems

URN to cite this document:
urn:nbn:de:bvb:355-epub-235787
DOI to cite this document:
10.5283/epub.23578
Treude, Jan-Hendrik ; Grant, James D. E.
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Date of publication of this fulltext: 19 Mar 2012 07:35


Abstract

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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