= Synchronous coordinates
{title2=$ds^2=c^2dt^2-h_{ij}(t,\mathbf x)dx^idx^j$}
In <synchronous coordinates>, fixed spatial-coordinate worldlines are <timelike geodesics>, and $t$ is their <proper time>. The metric has unit <lapse function> and zero <shift vector> in time units consistent with the displayed factor $c^2$. Indeed $g_{tt}=c^2$ and $g_{ti}=0$ give $\Gamma^\mu{}_{tt}=0$. Locally, an irrotational freely falling congruence permits this construction before crossings of the coordinate worldlines. <Comoving observers> in a <Friedmann-Lemaître-Robertson-Walker metric> provide the standard cosmological example.
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