Absence of Static, Spherically Symmetric Black Hole Solutions for   Einstein-Dirac-Yang/Mills Equations with Complete Fermion Shells
  We study a static, spherically symmetric system of (2j+1) massive Dirac particles, each having angular momentum j, j=1,2,..., in a classical gravitational and SU(2) Yang-Mills field. We show that for any black hole solution of the associated Einstein-Dirac-Yang/Mills equations, the spinors must vanish identically outside of the event horizon. 
Felix Finster, Joel Smoller, and Shing-Tung Yau