Congruence (general relativity)

In general relativity, a congruence (more properly, a congruence of curves) is the set of integral curves of a (nowhere vanishing) vector field in a four-dimensional Lorentzian manifold which is interpreted physically as a model of spacetime. Often this manifold will be taken to be an exact or approximate solution to the Einstein field equation.

Congruences generated by nowhere vanishing timelike, null, or spacelike vector fields are called timelike, null, or spacelike respectively.

A congruence is called a geodesic congruence if the tangent vector field ${\displaystyle {\vec {X}}}$ has vanishing covariant derivative, ${\displaystyle \nabla _{\vec {X}}{\vec {X}}=0}$.

...
Wikipedia