Causal structure

Causal structure is the pattern of which events can influence one another through causal curves. In relativity, it is determined by the spacetime metric’s light cones.

Spacetime: The four-dimensional setting in which events have spatial and temporal relations. Causal structure specifies which event relations spacetime permits.
Causal past and future: The sets of events that can send causal signals to, or receive them from, a given event. They express causal structure globally for individual events.
Cauchy problem: The problem of determining a system’s evolution from initial data on a specified surface. Causal structure determines whether initial data can govern later events.
Conformal geometry: The geometry preserved under local rescaling of lengths while angles and null directions remain fixed. Causal structure determines conformal geometry under suitable conditions, but not overall scale.
Event (relativity): A point in spacetime identified by a location and a time. Causal structure describes possible influences between spacetime events.
Causal relation: A relation in which one event can influence another along a future-directed causal curve. It turns allowed causal curves into an ordering of spacetime events.
Domain of dependence: The region whose events are determined by data on a given initial surface. Its boundary is set by causal curves and limits prediction.
Conformal transformation: A transformation that rescales a metric by a positive position-dependent factor. It can change measured durations and distances without changing light cones.
Light cone: The set of directions that light can travel from or toward an event in spacetime. Its boundaries divide events into causally reachable and unreachable regions.
Closed timelike curve: A timelike path through spacetime that returns to its starting event. Its existence permits causal loops and disrupts ordinary causal ordering.

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