  We prove the possibility of existence of stationary bound states of spin-half
particles in the Reissner-Nordstroem gravitational field using a self-conjugate
Hamiltonian with a flat scalar product of wave functions. Bound states of Dirac
particles with a real discrete energy spectrum can exist both for particles
above the external "event horizon", and for particles under the internal "event
horizon", or the Cauchy horizon. The Hilbert condition g_{00}>0 leads to a
boundary condition such that components of the vector of current density of
Dirac particles are zero near the "event horizons". Based on the results of
this study, we can assume that there exists a new type of charged collapsars,
for which the Hawking radiation is not present. The results of this study can
lead to a revision of some concepts of the standard cosmological model related
to the evolution of the universe and interaction of charged collapsars with
surrounding matter.
