The causal hierarchy of spacetimes

Abstract

The full causal ladder of spacetimes is constructed, and their updated main properties are developed. Old concepts and alternative definitions of each level of the ladder are revisited, with emphasis in minimum hypotheses. The implications of the recently solved ``folk questions on smoothability'', and alternative proposals (as recent isocausality), are also summarized.

Latex2e, 63 pages, 14 figures, uses psfrag. Contribution to the Proceedings of the ESI semester ``Geometry of Pseudo-Riemannian Manifolds with Applications in Physics'' (Vienna, 2006). Some erratas corrected and other modifications, including two references. This version matches the one to be published at the proceedings

References in corpus (3)

• On smooth Cauchy hypersurfaces and Geroch's splitting theorem
• A Causal Order for Spacetimes with $C^0$ Lorentzian Metrics: Proof of Compactness of the Space of Causal Curves
• No time machines in classical general relativity

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• Generalized cones as Lorentzian length spaces: Causality, curvature, and singularity theorems
• A Note on Non-compact Cauchy surface
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• Quantum Fields on Causal Sets
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• Causality of spacetimes admitting a parallel null vector and weak KAM theory
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• The Nature of Time: from a Timeless Hamiltonian Framework to Clock Time of Metrology
• The Contact Structure in the Space of Light Rays
• Green Operators in Low Regularity Spacetimes and Quantum Field Theory
• On Global Hyperbolicity of Spacetimes: Topology Meets Functional Analysis
• An Observer's View on Relativity: Space-Time Splitting and Newtonian Limit
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• Quantum fields on semi-globally hyperbolic space-times
• On the splitting problem for Lorentzian manifolds with an $\mathbb{R}$-action with causal orbits
• Causal and Topological Aspects in Special and General Theory of Relativity
• Constant Mean Curvature Foliations of $3$-Dimensional Twisted Product Spacetimes
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• Causal Classification of Conformally Flat Lorentzian Cylinders
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