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Non-existence of time-periodic solutions of the Dirac equation in a Reissner-Nordstrm black hole background

Felix Finster Joel Smoller Shing-Tung Yau

Mathematical Physics mathscidoc:1912.43528

Journal of Mathematical Physics, 41, (4), 2173-2194, 2000.4
It is shown analytically that the Dirac equation has no normalizable, time-periodic solutions in a ReissnerNordstrm black hole background; in particular, there are no static solutions of the Dirac equation in such a background metric. The physical interpretation is that Dirac particles can either disappear into the black hole or escape to infinity, but they cannot stay on a periodic orbit around the black hole.
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@inproceedings{felix2000non-existence,
  title={Non-existence of time-periodic solutions of the Dirac equation in a Reissner-Nordstrm black hole background},
  author={Felix Finster, Joel Smoller, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203830182663092},
  booktitle={Journal of Mathematical Physics},
  volume={41},
  number={4},
  pages={2173-2194},
  year={2000},
}
Felix Finster, Joel Smoller, and Shing-Tung Yau. Non-existence of time-periodic solutions of the Dirac equation in a Reissner-Nordstrm black hole background. 2000. Vol. 41. In Journal of Mathematical Physics. pp.2173-2194. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203830182663092.
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