  We consider a static, spherically symmetric system of a Dirac particle in a
classical gravitational and SU(2) Yang-Mills field. We prove that the only
black-hole solutions of the corresponding Einstein-Dirac-Yang/Mills equations
are the Bartnik-McKinnon black-hole solutions of the SU(2) Einstein-Yang/Mills
equations; thus the spinors must vanish identically. This indicates that the
Dirac particles must either disappear into the black-hole or escape to
infinity.
