Global Hyperbolicity and Completeness
General Relativity and Quantum Cosmology
2009-11-07 v2
Abstract
We prove global hyperbolicity of spacetimes under generic regularity conditions on the metric. We then show that these spacetimes are timelike and null geodesically complete if the gradient of the lapse and the extrinsic curvature are integrable. This last condition is required only for the tracefree part of if the universe is expanding.
Cite
@article{arxiv.gr-qc/0201057,
title = {Global Hyperbolicity and Completeness},
author = {Yvonne Choquet-Bruhat and Spiros Cotsakis},
journal= {arXiv preprint arXiv:gr-qc/0201057},
year = {2009}
}
Comments
7 pages. Accepted for publication in the Journal of Geometry and Physics. v2: Minor typos corrected