  We consider for j=1/2, 3/2,... a spherically symmetric, static system of
(2j+1) Dirac particles, each having total angular momentum j. The Dirac
particles interact via a classical gravitational and electromagnetic field.
  The Einstein-Dirac-Maxwell equations for this system are derived. It is shown
that, under weak regularity conditions on the form of the horizon, the only
black hole solutions of the EDM equations are the Reissner-Nordstrom solutions.
In other words, the spinors must vanish identically. Applied to the
gravitational collapse of a "cloud" of spin-1/2-particles to a black hole, our
result indicates that the Dirac particles must eventually disappear inside the
event horizon.
