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[itex]\nabla_{μ}R^{\mu\nu}=\nabla_{μ}R^{\mu\nu}[/itex]

insert the multiplicative identity, expressed as the product of the covariant and contravariant metric

[itex]\nabla_{μ}R^{\mu\nu}=\nabla_{μ}(g^{\mu \nu}g_{\mu\nu})R^{\mu\nu}[/itex]

contract the indices of the Ricci Tensor, to get

[itex]\nabla_{μ}R^{\mu\nu}=\nabla_{μ}g^{\mu\nu}R[/itex]

but the general theory tells us that

[itex]\nabla_{μ}R^{\mu\nu}=\frac{1}{2} \nabla_{μ}g^{\mu\nu}R[/itex]

Where have I gone wrong?

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# Einstein Tensor; super simple derivation; where did I go wrong?

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