paper

Equations of Motion in Kaluza-Klein Gravity Revisited

arXiv:gr-qc/0104008

Abstract

We discuss the equations of motion of test particles for a version of Kaluza-Klein theory where the cylinder condition is not imposed. The metric tensor of the five-dimensional manifold is allowed to depend on the fifth coordinate. This is the usual working scenario in brane-world, induced-matter theory and other Kaluza-Klein theories with large extra dimensions. We present a new version for the fully covariant splitting of the 5D equations. We show how to change the usual definition of various physical quantities in order to make physics in 4D invariant under transformations in 5D. These include the redefinition of the electromagnetic tensor, force and Christoffel symbols. With our definitions, each of the force terms in the equation of motion is gauge invariant and orthogonal to the four-velocity of the particle. The "hidden" parameter associated with the rate of motion along the extra dimension is identified with the electric charge, regardless of whether there is an electromagnetic field or not. In addition, for charged particles, the charge-to-mass ratio should vary. Therefore, the motion of a charged particle should differ from the motion of a neutral particle, with the same initial mass and energy, even in the absence of electromagnetic field. These predictions have important implications and could in principle be experimentally detected.

arXiv commentEffects from an extra dimension are discussed in a separated section (Sec. 7). References added. To appear in Gravitation & Cosmology

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