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.
Global hyperbolicity is stable in the interval topology / Minguzzi, Ettore; Benavides Navarro, J. J.. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - STAMPA. - 52:(2011), pp. 112504-1-112504-8. [10.1063/1.3660684]
Global hyperbolicity is stable in the interval topology
MINGUZZI, ETTORE;
2011
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.File | Dimensione | Formato | |
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Benavides and Minguzzi - Global hyperbolicity is stable in the interval topology - J. Math. Phys. 52 (2011) 112504.pdf
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