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MiS Preprint Repository

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MiS Preprint
37/1999

Non-existence of time-periodic solutions of the Dirac equation in an axisymmetric black hole geometry

Felix Finster, Niky Kamran, Joel Smoller and Shing-Tung Yau

Abstract

We prove that, in the non-extreme Kerr-Newman black hole geometry, the Dirac equation has no normalizable, time-periodic solutions. A key tool is Chandrasekhar's separation of the Dirac equation in this geometry. A similar non-existence theorem is established in a more general class of stationary, axisymmetric metrics in which the Dirac equation is known to be separable. These results indicate that, in contrast with the classical situation of massive particle orbits, a quantum mechanical Dirac particle must either disappear into the black hole or escape to infinity.

Received:
May 31, 1999
Published:
May 31, 1999

Related publications

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

Nonexistence of time-periodic solutions of the Dirac equation in an axisymmetric black hole geometry

In: Communications on pure and applied mathematics, 53 (2000) 7, pp. 902-929