Geodesic Deviation in Kaluza-Klein Theories
Richard Kerner, Jerome Martin, Salvatore Mignemi, Jan-Willem van, Holten
TL;DR
This paper analyzes geodesic deviation in Kaluza-Klein theories, showing that 4D projections match equations with Lorentz force, given an additional constraint on the deviation vector's fifth component.
Contribution
It provides a detailed derivation of geodesic deviation equations in multidimensional Kaluza-Klein models, clarifying their relation to 4D physics with electromagnetic forces.
Findings
4D projections of geodesic deviation match Lorentz force equations
An extra constraint on the fifth component of the deviation vector is necessary
The analysis bridges multidimensional theories with observable 4D physics
Abstract
We study in detail the equations of the geodesic deviation in multidimensional theories of Kaluza-Klein type. We show that their 4-dimensional space-time projections are identical with the equations obtained by direct variation of the usual geodesic equation in the presence of the Lorentz force, provided that the fifth component of the deviation vector satisfies an extra constraint derived here.
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