= Tidal acceleration
{title2=$a_{\mathrm{rel}}^a=-R^a{}_{bcd}U^b\xi^cU^d$}
The relative acceleration of neighboring freely falling bodies is measured by <geodesic deviation>, comparing their infinitesimal separation $\xi$ in a <parallel transport> frame along a reference <timelike geodesic> with tangent $U$. With $R^a{}_{bcd}$ defined by the <covariant derivative> commutator, it has the displayed form. In the <Newtonian limit> the corresponding <tidal tensor> is the spatial gradient of the <gravitational acceleration>. A single freely falling body can remove local gravitational acceleration by its frame choice, whereas relative tidal acceleration measures <curvature>.
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