I want to show that ∇(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}ϕ=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 (ℝ^{4},g) .

(a) Show, that R^ corresponds to - (∂ϕ/∂xμ∂xν)eμ ⊗ eν. The tidal force tensor of Newtonian physics.

(b) Show Ric(∂4, ∂4)= ∇^{2}ϕ.

(c) Show that , in the sense of the convections ,the Einstein tensor G becomes 2∇^{2}ϕ .

Please help me to understand how Einstein field equation becomes the Poisson equation?

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# How Einstein field equation becomes the Poisson equation?

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