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I have read many derivations of Einstein field equations (done one myself), but none of them explain why the constant term should have a $$c^4$$ in the denominator. the 8πG term can be obtained from Poisson's equation, but how does c^4 pop up? Most of the books just derive it with $$8\pi G$$, and say that in units where c is not equal to 1, you get $$8πG/c^4$$, even though there is no mention of an explicit assumption that c=1. They kind of just bring it up suddenly, and there is no prior need to assume c=1 anyway. I don't want to do it with Einstein-Hilbert action, but the standard $$G_{\mu\nu}=kT_{\mu\nu}$$ approach, where I need to show that $$k=\frac{8\pi G}{c^4}$$.

Thanks in advance!!

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# Derivations of Einstein field equations

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