Completeness of inextensible electromagnetic trajectories in a stationary spacetime

A new technique is introduced to study the completeness of inextensible electromagnetic trajectories in an n(≥2)-dimensional stationary spacetime. Sufficient conditions on an electromagnetic field on a stationary spacetime are imposed to ensure that the associated (n+1)-dimensional Kaluza-Klein bundle spacetime is itself stationary. The problem is then reduced to the geodesic completeness of the corresponding Kaluza-Klein bundle spacetime. Applications are given specially to the case of a standard static spacetime.