Absence of Static, Spherically Symmetric Black Hole Solutions for Einstein-Dirac-Yang/Mills Equations with Complete Fermion Shells

TL;DR

This paper proves that static, spherically symmetric black hole solutions cannot support non-trivial Dirac fermion shells in Einstein-Dirac-Yang/Mills systems, implying such fermionic matter cannot exist outside the horizon.

Contribution

It demonstrates the absence of static, spherically symmetric black hole solutions with non-trivial Dirac fermion shells in Einstein-Dirac-Yang/Mills equations.

Findings

Dirac spinors must vanish outside the event horizon in these solutions

No static, spherically symmetric black hole can support fermion shells

Supports the no-hair conjecture for fermionic matter in this context

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.