Absence of static, spherically symmetric black hole solutions for Einstein-Dirac-Yang/Mills equations with complete fermion shells

Abstract

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.