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.
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