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Linear waves in the Kerr geometry: a mathematical voyage to black hole physics

Felix Finster Niky Kamran Joel Smoller Shing-Tung Yau

Theoretical Physics mathscidoc:1912.43590

Bulletin of the American Mathematical Society, 46, (4), 635-659, 2009
This paper gives a survey of wave dynamics in the Kerr space-time geometry, the mathematical model of a rotating black hole in equilibrium. After a brief introduction to the Kerr metric, we review the separability properties of linear wave equations for fields of general spin s= 0,rac {1}{2}, 1, 2, corresponding to scalar, Dirac, electromagnetic fields and linearized gravitational waves. We give results on the long-time dynamics of Dirac and scalar waves, including decay rates for massive Dirac fields. For scalar waves, we give a rigorous treatment of superradiance and describe rigorously a mechanism of energy extraction from a rotating black hole. Finally, we discuss the open problem of linear stability of the Kerr metric and present partial results.
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@inproceedings{felix2009linear,
  title={Linear waves in the Kerr geometry: a mathematical voyage to black hole physics},
  author={Felix Finster, Niky Kamran, Joel Smoller, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204305415830154},
  booktitle={Bulletin of the American Mathematical Society},
  volume={46},
  number={4},
  pages={635-659},
  year={2009},
}
Felix Finster, Niky Kamran, Joel Smoller, and Shing-Tung Yau. Linear waves in the Kerr geometry: a mathematical voyage to black hole physics. 2009. Vol. 46. In Bulletin of the American Mathematical Society. pp.635-659. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204305415830154.
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