Chronological spacetimes without lightlike lines are stably causal

Abstract

The statement of the title is proved. It implies that under physically reasonable conditions, spacetimes which are free from singularities are necessarily stably causal and hence admit a time function. Read as a singularity theorem it states that if there is some form of causality violation on spacetime then either it is the worst possible, namely violation of chronology, or there is a singularity. The analogous result: "Non-totally vicious spacetimes without lightlike rays are globally hyperbolic" is also proved, and its physical consequences are explored.

20 pages, 6 figures

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• Spacetime Singularities
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• K-causality coincides with stable causality
• Raychaudhuri equation and singularity theorems in Finsler spacetimes
• Elements of causality theory
• Geometry of Schroedinger Space-Times II: Particle and Field Probes of the Causal Structure
• Geometry of weighted Lorentz-Finsler manifolds I: Singularity theorems
• On the Gannon-Lee Singularity Theorem in Higher Dimensions
• On the global existence of time
• A new singularity theorem for black holes which allows chronology violation in the interior
• The boundary of the chronology violating set
• Causal Cones, Cone Preserving Transformations and Causal Structure in Special and General Theory of Relativity
• Augustine of Hippo's philosophy of time meets general relativity
• Widening the light cones on subsets of spacetime: some variations to stable causality
• Isometries of spacetimes without observer horizons
• Cosmological singularities from high matter density without global topological assumptions
• Observations and predictions from past lightcones
• Causal and Topological Aspects in Special and General Theory of Relativity