Newtonian limit of general relativity
= Newtonian limit of general relativity
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= Newtonian limit
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For a weak, static field produced by nonrelativistic matter, $T_{00}=\rho$ is the dominant stress-energy component. The field equations and the slow-particle <geodesic equation> imply
$$
h_{00}=-2\Phi,
\qquad
\kappa=8\pi G,
$$
where the <Poisson equation> is $\nabla^2\Phi=4\pi G\rho$.