Cauchy Surface

Intuitively, a Cauchy surface is a plane in space-time which is like an instant of time; its significance is that giving the initial conditions on this plane determines the future (and the past) uniquely.

More precisely, a Cauchy surface is any subset of space-time which is intersected by every non-spacelike, inextensible curve, i.e. any causal curve, exactly once.

A partial Cauchy surface is a hypersurface which is intersected by any causal curve at most once.

The name is for Augustin Louis Cauchy.

Read more about Cauchy Surface:  Discussion, Cauchy Horizon

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