I've always found that the lagrangian for the Gravitational field is that from the Einstein-Hilbert action:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]L=R[/itex] (R is the Ricci scalar; I'm not including the factor of [itex]\sqrt{-g}[/itex])

but when variational principles are applied, we get the vacuum field equations (obviously). I'd like someone to tell me which would be the FULL lagrangian (with matter coupled) for getting the Einstein's field equations.

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# Lagrangian for the General Relativity

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