  We prove the possibility of existence of stationary bound states of
stationary bound states of spin-half probe particles for the Kerr and
Kerr-Newman gravitational fields using Chandrasekhar's Hamiltonian. If the
Hilbert condition is satisfied, g_{00}>0, bound states of Dirac particles with
a real discrete energy spectrum can exist both for particles outside the
surface of the outer ergosphere of the Kerr and Kerr-Newman fields, and for
particles under the surface of the inner ergosphere. In this case, the surfaces
of the external and internal ergospheres play the role of infinitely high
potential barriers. Spin-half quantum-mechanical particles cannot cross the
ergosphere surfaces of the Kerr and Kerr-Newman fields. Based on the results of
this study, we can assume that there exists a new type of rotating collapsars,
for which the Hawking radiation is absent. 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 rotating collapsars with
surrounding matter.
