# Einstein-Hilbert action and Lagrangian density for vacuum

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## Main Question or Discussion Point

From the action ∫Ldt =∫ι√|g|d4x where |g| is the determinant of the metric .and ι the lagrangian density.
For gravitational field why is this ι is replaced by the Ricci scaler R which yield field equations in vaccum.(Rij-1/2Rgij)=0
Is it that the lagrangian density corresponding to vaccum is the Ricci scaler??