Elements of causality theory

Abstract

These notes present some elements of causality theory. While they are not as complete as other treatments of the topic, there is some originality in that the whole approach is based on a definition of causal curves which allows to simplify many arguments. We keep track of the differentiability needed for various statements, obtaining a coherent theory for twice-continuously-differentiable metrics.

References in corpus (4)

• The causal hierarchy of spacetimes
• On Lorentzian causality with continuous metrics
• Chronological spacetimes without lightlike lines are stably causal
• On Ricci coefficients of null hypersurfaces with time foliation in Einstein vacuum space-time

Cited by in corpus (14)

• On Lorentzian causality with continuous metrics
• Convex neighborhoods for Lipschitz connections and sprays
• Light Rays, Singularities, and All That
• Timelike completeness as an obstruction to $C^0$-extensions
• Hawking's singularity theorem for $C^{1,1}$-metrics
• On differentiability of volume time functions
• The singularity theorems of General Relativity and their low regularity extensions
• Every Lipschitz metric has $C^1$-geodesics
• The exponential map of a $C^{1,1}$-metric
• Weakly trapped surfaces in asymptotically de Sitter spacetimes
• Uniqueness and non-uniqueness results for spacetime extensions
• Green Operators in Low Regularity Spacetimes and Quantum Field Theory
• On maximal globally hyperbolic vacuum space-times
• Attractors in spacetimes and time functions