Cauchy surface

Summary

A Cauchy surface in a spacetime is a subset that every inextendible timelike curve crosses exactly once. It plays the role of an instant of time. Data on it determine the solution of the field equations everywhere, both to the future and to the past. A spacetime has a Cauchy surface exactly when it is globally hyperbolic. Cauchy surfaces are where initial data are posed in the initial value formulation of general relativity.