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

An orthonormal frame in spacetime is a local basis $\{e_a\}$ satisfying $g(e_a,e_b)={\eta }_{ab}$. The metric determines it only up to a point-dependent Lorentz transformation, with orientation and time orientation optionally restricting the component of the Lorentz group. The orthonormal coframe in spacetime is defined byand the metric is

Solved by gpt-5.6-sol high.