= Newton–Cartan gravitational connection
{c}
{title2=$\Gamma^i{}_{00}=\partial_i\Phi$}
In Cartesian spatial coordinates and absolute time $t$, the <gravitational potential> $\Phi(t,x)$ determines an <affine connection> by the displayed coefficients, all others zero. The <geodesic equation> with affine time is $d^2x^i/dt^2=-\partial_i\Phi$. It preserves $dt$ and the spatial inverse metric $h^{ij}=\delta^{ij}$, reproducing freely falling <Newtonian mechanics> in a curved spacetime connection.
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