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The Einstein field equation relates the curvature of space-time to the energy tensor of mass-energy. This is fine. These field equations are derived by varying the Hilbert action. Now the Hilbert action is an integral of scalar curvature (R) over volume. So, when we vary this action, we must get the energy tensor of the field. How then do we naively take this to be the energy tensor of mass-energy and claim to have derived the field equation?

Thank you!

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# Energy tensor in the Field Equation

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