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lili 73
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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?
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?