Global hyperbolicity is stable in the interval topology

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.

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

References in corpus (4)

• Globally hyperbolic spacetimes can be defined as "causal" instead of "strongly causal"
• The causal hierarchy of spacetimes
• The causal ladder and the strength of K-causality. II
• Global hyperbolicity is stable in the interval topology

Cited by in corpus (14)

• Causality theory for closed cone structures with applications
• On Lorentzian causality with continuous metrics
• The Penrose singularity theorem in regularity $C^{1,1}$
• The representation of spacetime through steep time functions
• On differentiability of volume time functions
• Global hyperbolicity is stable in the interval topology
• Algebraic Structure of Classical Field Theory: Kinematics and Linearized Dynamics for Real Scalar Fields
• Characteristics, Conal Geometry and Causality in Locally Covariant Field Theory
• Globally hyperbolic spacetimes: slicings, boundaries and counterexamples
• On the space of light rays of a space-time and a reconstruction theorem by Low
• Further observations on the definition of global hyperbolicity under low regularity
• Green Operators in Low Regularity Spacetimes and Quantum Field Theory
• Lorentzian manifolds properly isometrically embeddable in Minkowski spacetime
• A note on stability and Cauchy time functions