Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 309 / 2 / b / ii / Solution

At the chosen event use the orthonormal frame in spacetime from the hint. The electromagnetic energy density isand the energy flux is the Poynting vector $\mathbf{S}=\mathbf{E}\times \mathbf{B}$. Depending on the index convention, the required contraction is $\rho -w{S}_1$ or $\rho +w{S}_1$. In either case,Rescaling $V$ and rotating the spatial frame covers arbitrary future timelike $V$ and future causal $W$. Thus the Maxwell field satisfies the dominant energy condition.