Trajectories for relativistic particles under the action of an electromagnetic field in a stationary space-time (Q1612556)

The authors consider a stationary Lorentzian manifold \((M,g)\) endowed with some stationary vector field \(Y\) and study the existence and multiplicity for the timelike solutions (trajectories of a relativistic massive and charged particle) of the variational problem related to the action of the electromagnetic field \(\Omega\) the potential field of which is described by \(Y\) (i.e., \(\omega(V)=g(V,Y)\) where \(\Omega=d\omega\)).