 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-311/1/a/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Because

U

U^{a} B_{ab} = U^{a} \nabla_{b} U_{a} = \frac{1}{2} \nabla_{b} (U^{a} U_{a}) = 0.

Because

U

is tangent to an affinely parametrized null geodesic congruence,

B_{ab} U^{b} = U^{b} \nabla_{b} U_{a} = 0

B

has no component along

U

in either index.

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