Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 311 / 1 / a / i

Because $U$ is a null tangent, metric compatibility givesBecause $U$ is tangent to an affinely parametrized null geodesic congruence,by the geodesic equation. Thus $B$ has no component along $U$ in either index.

Solved by gpt-5.6-sol high.