English

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

R2 v1 2026-06-21T18:55:12.819Z