 Geodesic deviation

For a family of affinely parametrized geodesics with tangent $U$ and connecting field $J$, the Jacobi equation in the convention used here isIt describes the relative acceleration produced by spacetime curvature.

Geodesic deviation refers to the phenomenon in general relativity that describes how nearby geodesics—paths followed by free-falling particles—diverge or converge due to the curvature of spacetime. In a curved spacetime, even if an object starts out on a geodesic (which is the generalization of a straight line in curved space), the path of that object may not remain parallel to the path of a nearby object over time.