Undergrad Kaluza–Klein metric, space between charged capacitor?

[Spinnor]

Consider empty spacetime containing a charged capacitor. Is there a simple expression for metric for the spacetime between the capacitor plates in terms of Kaluza–Klein theory?

We are told that spacetime tells matter how to move; matter tells spacetime how to curve. Is there a Kaluza–Klein version of this as it might deal with the space between a charged capacitor? Something like, curved 5 dimensional spacetime tells charged matter how to move and charged matter tells 5 dimensional spacetime how to curve?

So if we have a charged particle between the plates of a charged capacitor we know the charged particle will move towards the opposite charged plate and away from the like charged plate. But in terms of Kaluza-Klein theory we are allowed to think that the charged particle between the charged capacitor moves in such a way to take the shortest path in 5D spacetime?

Thanks!

 

[mitchell porter]

In the appendix of Kerner et al, you can see how to embed a desired electromagnetic potential into a 5d metric, so that 5d geodesic motion gives you 4d gravity + electromagnetism, for a particle with a given ratio of charge to mass.

However, no-one ever found a good KK model for charge as an electromagnetic source. The small radius of the fifth dimension seems to imply that the electrically charged test particles that follow the geodesic equation, have a Planck mass; and if you consider purely gravitational solitons as a model of matter, you get magnetic monopoles.