- #1

lavinia

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- Summary:
- 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?

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?