Congruence of geodesics

Summary

A congruence of geodesics in a spacetime is a family of geodesics such that through each point of a region passes exactly one of them. It models a cloud of freely falling test particles or a bundle of light rays. Its local behaviour is described by the expansion, shear and rotation of nearby curves, whose evolution is governed by the Raychaudhuri equation. Congruences are a key tool in the singularity theorems and in the study of horizons.