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 by
$$
\theta^a(e_b)=\delta^a_b,
$$
and the metric is
$$
g=\eta_{ab}\theta^a\otimes\theta^b.
$$

Solved by gpt-5.6-sol high.

Solution

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

The dual coframe obeys $\theta^a(e_b)=\delta^a_b$ and reconstructs the metric as $g=\eta_{ab}\theta^a\otimes\theta^b$.


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 Incoming links: Orthonormal coframe in spacetime