Let there be Newtonian Gravity:
L ( x , t ) = − 1 8 π G | ∇ Φ ( x , t ) | 2 − ρ ( x , t ) Φ ( x , t ) {\displaystyle {\mathcal {L}}(\mathbf {x} ,t)=-{1 \over 8\pi G}|\nabla \Phi (\mathbf {x} ,t)|^{2}-\rho (\mathbf {x} ,t)\Phi (\mathbf {x} ,t)}