Solution
= Solution
A <null geodesic congruence> is a smooth family of nonintersecting null geodesics filling an open spacetime region. For its affinely parametrized tangent $U^a$,
$$
U^aU_a=0,
\qquad
U^b\nabla_bU^a=0.
$$
Writing $B_{ab}=\nabla_bU_a$, differentiation of the null norm and the <geodesic equation> give respectively
$$
U^aB_{ab}=\frac12\nabla_b(U^aU_a)=0,
\qquad
B_{ab}U^b=U^b\nabla_bU_a=0.
$$