in that book ,the author use a native spacetime (ℝ4,g) with g,
g=-(1+2 ϕ)du4⊗ du4+(1-2 ϕ)\sumduα⊗ duα ,where ϕ:ℝ3→ℝ will be interpreted as a time –independent Newtonian gravitational potential .
(sigma from 1 to 3).
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...