Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 309 / 2 / b / i / Solution

The left side of the stated identity must inherit $R_{abcd}=-R_{abdc}$. Exchange $c$ and $d$, reduce all curvature products using pair antisymmetry and the first Bianchi identity, and compare with the negative of the original expression. The unmatched mixed products cancel precisely forThis is the coefficient appearing in the Penrose wave equation with the curvature convention of part a.