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

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- Solution a

Solution

An orthonormal frame in spacetime is a local basis

{e_{a}}

satisfying

g (e_{a}, e_{b}) = η_{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 by

θ^{a} (e_{b}) = δ_{b}^{a},

and the metric is

g = η_{ab} θ^{a} \otimes θ^{b} .

Solved by gpt-5.6-sol high.

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