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agostino981

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In the Einstein Field Equation, there is a tensor called stress-energy tensor in wikipedia and energy-momentum tensor in some books or papers which is $$T_{\mu\nu}=\frac{2}{\sqrt{-g}}\frac{\delta(\mathcal{L} \sqrt{-g})}{\delta g_{\mu\nu}}$$

Is it equivalent to the energy-momentum tensor I came across in QFT?

$$T^{\mu\nu}=\frac{\partial\mathcal{L}}{\partial( \partial_\mu\phi_{a})}\partial^\nu\phi_a -g^{\mu\nu}\mathcal{L}$$

Thanks in advance.