Given a metric gμν, one can select an orthonormal basis ωˆa such that, ds2=ωˆt⊗ωˆt−ωˆx⊗ωˆx−...
By employing the Cartan structural equations, one can 'read off' the components of the Ricci tensor and Riemann curvature tensor in the orthonormal basis. My question is: how do I take my curvature tensors in the orthonormal basis back to the coordinate basis after?
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