  Nondecaying bound states of elementary spin-half particles are validated and
calculated numerically for the Schwarzschild gravitational field using a
self-conjugate Hamiltonian with a flat scalar product for any value of the
gravitational coupling constant. 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 horizon". At small values of the coupling
constant, the energy spectrum is close to the hydrogen-like spectrum. Based on
the results of this study, we can assume that there exists a new type of
collapsars, for which the Hawking radiation mechanism is not present. From the
standpoint of cosmology, if the value of the gravitational coupling constant is
small, alpha<<1, the new type of nonradiating relict collapsars can manifest
itself only through gravitation. Thus, they are good candidates for the role of
"dark matter" carriers. In the wide range of admissible masses, there can exist
collapsars of a new type with the masses of hypothesized WIMP particles, which
are treated as representatives of "dark matter" in numerous scenarios of the
expansion of the universe. The results of this study can lead to revisiting
some concepts of the standard cosmological model related to the evolution of
the universe and interaction of collapsars with surrounding matter.
