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Einstein tensor On a pseudo-Riemannian manifold (M, g), the tensorGµν = Rµν− 12Rgµν where Rµν is the Ricci tensor and R is the Ricci scalar of the Levi-Civita connection of the metric g.

By extension, on a manifold M with a connection Nαβµ, it is the tensor with the same local expression where Rµν is now the Ricci tensor and R is the Ricci scalar of the connection fixed on M .