Volume Comparison for Hypersurfaces in Lorentzian Manifolds and Singularity Theorems
General Relativity and Quantum Cosmology
2013-03-19 v1 Mathematical Physics
Differential Geometry
math.MP
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.
Cite
@article{arxiv.1201.4249,
title = {Volume Comparison for Hypersurfaces in Lorentzian Manifolds and Singularity Theorems},
author = {Jan-Hendrik Treude and James D. E. Grant},
journal= {arXiv preprint arXiv:1201.4249},
year = {2013}
}
Comments
15 pages, LaTeX