Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 309 / 2 / a

An infinitesimal coordinate change generated by ${\xi }_a$ acts on the trace-reversed metric perturbation asIts divergence changes bySolving $\square {\xi }_b={\partial }^a{\bar{h}}_{ab}$ therefore imposes Lorenz gauge in linearized gravity, ${\partial }^a{\bar{h}}_{ab}=0$. Transformations satisfying $\square {\xi }_b=0$ remain and form the residual gauge symmetry of linearized gravity.

Solved by gpt-5.6-sol high.