Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 309 / 3 / d / Solution

In the orthonormal frame choose the null vector $k=e_0+e_2$, which has a nonzero angular component. The curvature forms giveFor a null vector, the trace term in the Einstein field equations drops out, so the null energy condition implies $R_{ab}{k}^a{k}^b\ge 0$. Therefore

Solved by gpt-5.6-sol high.