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Tensor calculus (tensor analysis) is a systematic extension of vector calculus to multivector and tensor fields in a form that is independent of the choice of coordinates on the relevant manifold, but which accounts for respective sub-spaces, their symmetries, and their connections.

4 votes

Can you get $g_{\mu\nu}$ from $R^\lambda_{\alpha\beta\gamma}$?

No, this is not possible. Finding the metric tensor requires finding a solution to the EFEs. It's important to understand that the Riemann tensor tells us how the metric tensor varies across some inte …
Logan J. Fisher's user avatar