General-relativistic radial motions of neutral and charged test particles in the field of a charged spherically symmetric object

General-relativistic radial motions of charged and neutral test particles in the Reissner-Nordström field are investigated and classified. The conditions for suspension of such particles over the central source and stability of such equilibrium static states are studied. It is shown that stable states are only possible for the bound states of weakly charged particles in the field of an extremely charged central source.