I have been recently trying to derive the Einstein tensor and stress energy momentum tensor for a certain traversable wormhole metric. In my multiple attempts at doing so, I used a coordinate basis. My calculations were correct, but the units of some of the elements of the stress energy momentum tensor were wrong because of the fact that angles don't have units of length like the radial coordinate and the temporal coordinate (ct). The metric is a spherical basis by the way. Anyway, I was told that I should use an orthonormal basis to derive the tensors as opposed to a coordinate basis. Now, in a coordinate basis, the steps to derive your relativistic tensors (assuming you already have your metric tensor and inverse metric tensor) are as follows: 1. Plug your metric and inverse metric tensors into the Christoffel symbol formula to get your Christoffel symbols: Γmij = ½ gmk [ ∂gki/∂xj + ∂gjk/∂xi - ∂gij/∂xk ] 2. Plug your Christoffel symbol into the Ricci tensor formula: Rbv= ∂Γavb/∂xa - ∂Γaab/∂xv + ΓaacΓcvb - ΓavcΓcab 3. Contract your Ricci tensor using an inverse metric tensor to get your curvature scalar: R= gbvRbv Then all you have to do is plug in all of these tensors into the Einstein field equations and you get the Einstein tensor. This was all in a coordinate basis. Apparently in an orthonormal basis however, the steps are as follows: 1. Get your metric tensor. 2. Derive some basis vectors. How to derive those basis vectors: Do gijdxidxj where dxi and dxj are treated as vectors instead of just coordinates. You must then make sure that this expression equals 0 whenever i ≠ j and this expression equals 1 whenever i = j . Example: If my metric tensor component g11 = sin(θ) then my basis vector e1 must be < 0, 1/squrt(sin(θ)) , 0, 0 > . This is because if you dot product this basis vector with itself and then multiply that dot product by g11, then the result will be 1. Of course this is assuming that your basis vector is orthogonal to the other ones. In short, that is how you derive your basis vectors (so I am told). Now my question to you is: What do I do next after I have derived these basis vectors if I am trying to get to stuff like the Christoffel symbol or any of the curvature tensors?