Dimensional Reduction of the 5D Kaluza-Klein Geodesic Deviation Equation

Details Dimensional Reduction of the 5D Kaluza-Klein Geodesic Deviation Equation Dimensional Reduction of the 5D Kaluza-Klein Geodesic Deviation Equation

2009-09-17

arxiv.org/abs/0909.3336v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages

Scientific paper

10.1007/s10714-009-0853-3

In the work of Kerner et al. (2001) the problem of the geodesic deviation in a 5D Kaluza Klein background is faced. The 4D space-time projection of the resulting equation coincides with the usual geodesic deviation equation in the presence of the Lorenz force, provided that the fifth component of the deviation vector satisfies an extra constraint which takes into account the $q/m$ conservation along the path. The analysis was performed setting as a constant the scalar field which appears in Kaluza-Klein model. Here we focus on the extension of such a work to the model where the presence of the scalar field is considered. Our result coincides with that of Kerner et al. when the minimal case $\phi=1$ is considered, while it shows some departures in the general case. The novelty due to the presence of $\phi$ is that the variation of the $q/m$ between the two geodesic lines is not conserved during the motion; an exact law for such a behaviour has been derived.

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