MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

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

Felix Finster, Joel Smoller and Shing-Tung Yau


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.


Related publications

2000 Repository Open Access
Felix Finster, Joel Smoller and Shing-Tung Yau

The interaction of Dirac particles with non-abelian gauge fields and gravity-black holes

In: The Michigan mathematical journal, 47 (2000) 1, pp. 199-208