  We show that a spin-1/2 particle in the gravitational field of a massive body
of radius R which slightly exceeds the Schwarzschild radius r_s, possesses a
dense spectrum of narrow resonances. Their lifetimes and density tend to
infinity in the limit R -> r_s. We determine the cross section of the particle
capture into these resonances and show that it is equal to the spin-1/2
absorption cross section for a Schwarzschild black hole. Thus black-hole
properties may emerge in a non-singular static metric prior to the formation of
a black hole.
