Volume comparison for hypersurfaces in Lorentzian manifolds and singularity theorems |
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| Authors: | Jan-Hendrik Treude James D E Grant |
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| Institution: | 1. Fakult?t für Mathematik, Universit?t Regensburg, 93040, Regensburg, Germany
2. Gravitationsphysik, Fakult?t für Physik, Universit?t Wien, Boltzmanngasse 5, 1090, Wien, Austria
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| 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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