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An integral spectral representation of the propagator for the wave equation in the Kerr geometry

Felix Finster Niky Kamran Joel Smoller Shing-Tung Yau

Mathematical Physics mathscidoc:1912.43570

Communications in mathematical physics, 260, (2), 257-298, 2005.12
We consider the scalar wave equation in the Kerr geometry for Cauchy data which is smooth and compactly supported outside the event horizon. We derive an integral representation which expresses the solution as a superposition of solutions of the radial and angular ODEs which arise in the separation of variables. In particular, we prove completeness of the solutions of the separated ODEs.
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@inproceedings{felix2005an,
  title={An integral spectral representation of the propagator for the wave equation in the Kerr geometry},
  author={Felix Finster, Niky Kamran, Joel Smoller, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204117163365134},
  booktitle={Communications in mathematical physics},
  volume={260},
  number={2},
  pages={257-298},
  year={2005},
}
Felix Finster, Niky Kamran, Joel Smoller, and Shing-Tung Yau. An integral spectral representation of the propagator for the wave equation in the Kerr geometry. 2005. Vol. 260. In Communications in mathematical physics. pp.257-298. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204117163365134.
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