uncommon questions - vanishing gravitational Lagrange-densities

Can you think of systems where the gravitational Lagrange density is zero, in analogy to the vanishing \(F_{\mu\nu}F^{\mu\nu}\) for vacuum solutions in electrodynamics? Would the example hold only for the Ricci-scalar \(R\) or for the terms \(\sqrt{-g}R\) or \(\Lambda\sqrt{-g}\) as well?