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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 Diracparticles interact via a classical gravitational and electromagnetic field.  The Einstein-Dirac-Maxwell equations for this system are derived. It is shownthat, under weak regularity conditions on the form of the horizon, the onlyblack hole solutions of the EDM equations are the Reissner-Nordstrom solutions.In other words, the spinors must vanish identically. Applied to thegravitational collapse of a "cloud" of spin-1/2-particles to a black hole, ourresult indicates that the Dirac particles must eventually disappear inside theevent horizon.Comment: 13 pages, LaTeX, typo in separation ansatz (3.1) and (3.2) correcte

Non-Existence of Black Hole Solutions¶for a Spherically Symmetric, Static Einstein-Dirac-Maxwell System