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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 (www.arxiv.org) 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
54/1998

Non-existence of black hole solutions for a spherically symmetric, static Einstein-Dirac-Maxwell system

Felix Finster, Joel Smoller and Shing-Tung Yau

Abstract

We consider for j=1/2, 3/2,... a spherically symmetric, static system of (2j+1) Dirac particles, each having total angular momentum j. The Dirac particles interact via a classical gravitational and electromagnetic field.

The Einstein-Dirac-Maxwell equations for this system are derived. It is shown that, under weak regularity conditions on the form of the horizon, the only black hole solutions of the EDM equations are the Reissner-Nordstrom solutions. In other words, the spinors must vanish identically. Applied to the gravitational collapse of a "cloud" of spin-1/2-particles to a black hole, our result indicates that the Dirac particles must eventually disappear inside the event horizon.

Received:
Nov 16, 1998
Published:
Nov 16, 1998

Related publications

inJournal
1999 Repository Open Access
Felix Finster, Joel Smoller and Shing-Tung Yau

Non-existence of black hole solutions for a spherically symmetric, static Einstein-Dirac-Maxwell system

In: Communications in mathematical physics, 205 (1999) 2, pp. 249-262