Causal structure

Summary

The causal structure of a Lorentzian manifold describes which events can influence which other events. It starts from the classification of tangent vectors into timelike, null and spacelike. It then consists of the relations of being reachable by a future-directed timelike curve, or by a future-directed causal curve. It depends only on the light cones, so it is unchanged when the metric is multiplied by a positive function. It is the language of global questions in general relativity: horizons, singularities, global hyperbolicity and time travel.