Non-Existence of Time-Periodic Solutions of the Dirac Equation in an Axisymmetric Black Hole Geometry

Details Non-Existence of Time-Periodic Solutions of the Dirac Equation in an Axisymmetric Black Hole Geometry Non-Existence of Time-Periodic Solutions of the Dirac Equation in an Axisymmetric Black Hole Geometry

1999-05-14

arxiv.org/abs/gr-qc/9905047v2

Commun.Pure Appl.Math. 53 (2000) 902-929, erratum Commun.Pure Appl.Math. 53 (2000) 1201

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

25 pages, 1 figure (published version), eigenvalues of angular momentum in direction of symmetry axis corrected to be half odd

Scientific paper

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.

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