Global hyperbolicity is stable in the interval topology
General Relativity and Quantum Cosmology
2011-12-06 v3
Abstract
We prove that global hyperbolicity is stable in the interval topology on the spacetime metrics. We also prove that every globally hyperbolic spacetime admits a Cauchy hypersurface which remains Cauchy under small perturbations of the spacetime metric. Moreover, we prove that if the spacetime admits a complete timelike Killing field, then the light cones can be widened preserving both global hyperbolicity and the Killing property of the field.
Keywords
Cite
@article{arxiv.1108.5120,
title = {Global hyperbolicity is stable in the interval topology},
author = {J. J. Benavides Navarro and E. Minguzzi},
journal= {arXiv preprint arXiv:1108.5120},
year = {2011}
}
Comments
14 pages, 2 figures. v2: shortened introduction; v3: added a note and a reference