The Interaction of Dirac Particles with Non-Abelian Gauge Fields and Gravity - Black Holes

TL;DR

This paper proves that in a static, spherically symmetric system involving Dirac particles, gravity, and SU(2) gauge fields, the only black-hole solutions are the known Einstein-Yang-Mills solutions, implying Dirac particles cannot form stable black-hole configurations.

Contribution

It demonstrates that Dirac particles cannot sustain non-trivial black-hole solutions in this setting, extending the understanding of matter interactions with gravity and gauge fields.

Findings

Dirac particles must vanish in black-hole solutions.

Only Einstein-Yang-Mills black holes exist with Dirac fields absent.

Dirac particles cannot form stable black-hole configurations in this context.

Abstract

We consider a static, spherically symmetric system of a Dirac particle in a classical gravitational and SU(2) Yang-Mills field. We prove that the only black-hole solutions of the corresponding Einstein-Dirac-Yang/Mills equations are the Bartnik-McKinnon black-hole solutions of the SU(2) Einstein-Yang/Mills equations; thus the spinors must vanish identically. This indicates that the Dirac particles must either disappear into the black-hole or escape to infinity.