Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 311 / 1 / a / i / Solution

A null geodesic congruence is a smooth family of nonintersecting null geodesics filling an open spacetime region. For its affinely parametrized tangent $U^a$,Writing $B_{ab}={\nabla }_b{U}_a$, differentiation of the null norm and the geodesic equation give respectively