Analysis of half-spin particle motion in static Reissner-Nordström and Schwarzschild fields

The paper presents the analysis of effective potentials of Dirac equations in static Schwarzschild and Reissner-Nordström (RN) fields. It is shown that in all the explored cases the condition of a particle "fall" to appropriate event horizons is fulfilled. The exception is one of the solutions for the Reissner-Nordström extremal field, for which the existence of the stationary bound state of half-spin particles is possible inside the event horizon. (paper)