I want to show that ∇2ϕ=ρ/2, which governs gravity in Newtonian physics? I found solution of this question in [General Relativity for Mathematicians, R.K.Sachs and H.Wu, 1997, page 112&271]. Solution refer to optional exercise as follows: Let R^ be the (0, 4) –tensor field physically equivalent to the curvature tensor of (ℝ4,g) . (a) Show, that R^ corresponds to - (∂ϕ/∂xμ∂xν)eμ ⊗ eν. The tidal force tensor of Newtonian physics. (b) Show Ric(∂4, ∂4)= ∇2ϕ. (c) Show that , in the sense of the convections ,the Einstein tensor G becomes 2∇2ϕ . Please help me to understand how Einstein field equation becomes the Poisson equation?