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!