Non-existence of black hole solutions for a spherically symmetric, static Einstein-Dirac-Maxwell system

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 sho wn that, under weak regularity conditions on the form of the horizon, the o nly black hole solutions of the EDM equations are the Reissner-Nordstrom so lutions. In other words, the spinors must vanish identically. Applied to th e gravitational collapse of a "cloud" of spin-1/2-particles to a black hole , our result indicates that the Dirac particles must eventually disappear i nside the event horizon.