Hey all, making my way through Landau and Lifgarbagez classical theory of fields and i had a specific question on the Einstein equations. Following the palatini approach, we assume that the connection and metric are independent variables and are not related(adsbygoogle = window.adsbygoogle || []).push({}); a priori. In the footnote, they say by calculating the variation of the gravitational action and requiring that it vanish,

[itex]\delta S_g=\int\left(R_{jk}-\frac{1}{2}g_{jk}R\right)\delta g^{jk}\sqrt{-g}d^4x[/itex]

we are supposedly able to determine the relation between the two. However, i am at a loss as to how they make this leap from what is given above.

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# Deriving the realtion between the connection and metric from the palatini formalism

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