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Physics
Special and General Relativity
Jacobi Fields & Tidal Forces
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[QUOTE="lavinia, post: 6364521, member: 243745"] [B]TL;DR Summary:[/B] Particles in free fall in a gravitational field feel a tidal force that pulls them towards each other, How does once describe this force mathematically? It would seem that some feature of associated Jacobi fields should give the answer. Given a one parameter family of geodesics, the variation vector field is a Jacobi field. Mathematically this means that the field, ##J##, satisfies the differential equation ## ∇_{V}∇_{V}J =- R(V,J,)V## where ##V## is the tangent vector field and ##R## is the curvature tensor and ##∇## is the covariant derivative operator. Suppose the variation through geodesics is a one parameter family of particles in free fall in a gravitational field. One would think that the tidal drift could be expressed in terms of the Jacobi field ##J##. If true, how is this done mathematically and what is the physical reasoning? [/QUOTE]
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Special and General Relativity
Jacobi Fields & Tidal Forces
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