: Mathématiques: geodesic deviation

geometry > differential geometry > Riemannian geometry > geodesic deviation

mathematical physics > general relativity > geodesic deviation

geodesic deviation

In general relativity, if two objects are set in motion along two initially parallel trajectories, the presence of a tidal gravitational force will cause the trajectories to bend towards or away from each other, producing a relative acceleration between the objects. Mathematically, the tidal force in general relativity is described by the Riemann curvature tensor, and the trajectory of an object solely under the influence of gravity is called a geodesic. The geodesic deviation equation relates the Riemann curvature tensor to the relative acceleration of two neighboring geodesics. In differential geometry, the geodesic deviation equation is more commonly known as the Jacobi equation.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Geodesic_deviation)

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