arXiv2026
Massive particle surfaces (MPS), introduced by Kobialko, Bogush and Gal'tsov, are timelike hypersurfaces confining the trajectories of charged massive particles with fixed Killing energy and charge-to-mass ratio, in analogy with the photon surfaces of Claudel, Virbhadra and Ellis. We study both classes in standard stationary spacetimes within a unified Finslerian framework. For Killing-invariant hypersurfaces $\mathbb{R}\times S_0$, with $S_0$ a hypersurface of a spacelike slice $S$, we prove that photon hypersurfaces and MPS are exactly those for which $S_0$ is totally geodesic with respect to the Fermat metric and to a Jacobi--Randers metric on $S$, respectively. For MPS we also give a gauge-invariant version, in terms of a Riemannian Jacobi metric and a tangency condition on the reduced magnetic field. For arbitrary timelike hypersurfaces, we give a coordinate-free formulation of the partial umbilicity characterization of MPS and, in dimension at least four and under a natural energy condition, we characterize when an MPS is quasi-umbilical in the sense of B.-Y. Chen. In the Som--Raychaudhuri spacetime of a rigidly rotating charged dust we exhibit MPS which are neither photon hypersurfaces nor quasi-umbilical. Finally, under completeness assumptions on the Jacobi--Randers metric, we prove existence and multiplicity results for proper-time parametrized solutions of the Lorentz force equation connecting a point to a flow line of the Killing field and, under compactness assumptions, existence of solutions with periodic spatial projection, possibly confined to an MPS.