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Nonexistence of timeperiodic solutions of the Dirac equation in an axisymmetric black hole geometry

Felix Finster Niky Kamran Joel Smoller Shing-Tung Yau

Theoretical Physics mathscidoc:1912.43531

Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences, 53, (7), 902-929, 2000.7
We prove that in the nonextreme KerrNewman black hole geometry, the Dirac equation has no normalizable, timeperiodic solutions. A key tool is Chandrasekhar's separation of the Dirac equation in this geometry. A similar nonexistence 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 to the classical situation of massive particle orbits, a quantum mechanical Dirac particle must either disappear into the black hole or escape to infinity. 2000 John Wiley & Sons, Inc.
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@inproceedings{felix2000nonexistence,
  title={Nonexistence of timeperiodic solutions of the Dirac equation in an axisymmetric black hole geometry},
  author={Felix Finster, Niky Kamran, Joel Smoller, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203841121687095},
  booktitle={Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences},
  volume={53},
  number={7},
  pages={902-929},
  year={2000},
}
Felix Finster, Niky Kamran, Joel Smoller, and Shing-Tung Yau. Nonexistence of timeperiodic solutions of the Dirac equation in an axisymmetric black hole geometry. 2000. Vol. 53. In Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences. pp.902-929. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203841121687095.
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