= Weak gravitational field
{title2=$|\phi|/c^2\ll1$}
A <weak gravitational field> is a regime in which the <metric> differs little from a suitable flat reference <metric>. In a slow-motion, approximately stationary situation, $g_{tt}\simeq1+2\phi/c^2$ for signature $(+---)$, with Newtonian potential $\phi$. Proper-<clock> rates then differ fractionally by $\Delta\phi/c^2$. Small <metric> perturbations do not by themselves imply every <velocity> is nonrelativistic; slow motion is a separate approximation when deriving Newtonian dynamics.
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