Global hyperbolicity is stable in the interval topology

Details Global hyperbolicity is stable in the interval topology Global hyperbolicity is stable in the interval topology

2011-08-25

arxiv.org/abs/1108.5120v3

Journal of Mathematical Physics 52, (2011) 112504

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, 2 figures. v2: shortened introduction; v3: added a note and a reference

Scientific paper

10.1063/1.3660684

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.

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