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Einstein Tensor

A contracted form of the Riemann tensor, simplifying calculations within the Einstein Field Equations and providing a compact representation.
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The statement of the theorem

Define the Ricci tensor RμνR_{\mu\nu} as the contraction of the Riemann tensor: \n\nRμν=RλμλνR_{\mu\nu} = R^{\lambda}{}_{\mu\lambda\nu} \n\nLet RR be the Ricci scalar, defined as the trace of the Ricci tensor: \n\nR=gμνRμνR = g^{\mu\nu} R_{\mu\nu} \n\nThe Einstein tensor GμνG_{\mu\nu} is then defined by the combination:\n\nGμν=Rμν−12gμνRG_{\mu\nu} = R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R
Source: Wikipedia