Volume Comparison for Hypersurfaces in Lorentzian Manifolds and Singularity Theorems

Details Volume Comparison for Hypersurfaces in Lorentzian Manifolds and Singularity Theorems Volume Comparison for Hypersurfaces in Lorentzian Manifolds and Singularity Theorems

2012-01-20

arxiv.org/abs/1201.4249v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, LaTeX

Scientific paper

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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