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Decay of solutions of the wave equation in the Kerr geometry

Felix Finster Niky Kamran Joel Smoller Shing-Tung Yau

Mathematical Physics mathscidoc:1912.43503

Communications in Mathematical Physics, 264, (2), 465-503, 2006.6
We consider the Cauchy problem for the massless scalar wave equation in the Kerr geometry for smooth initial data compactly supported outside the event horizon. We prove that the solutions decay in time in <i>L</i> <sup></sup> <sub>loc</sub>. The proof is based on a representation of the solution as an infinite sum over the angular momentum modes, each of which is an integral of the energy variable <i></i> on the real line. This integral representation involves solutions of the radial and angular ODEs which arise in the separation of variables.
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@inproceedings{felix2006decay,
  title={Decay of solutions of 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/20191224203644260670067},
  booktitle={Communications in Mathematical Physics},
  volume={264},
  number={2},
  pages={465-503},
  year={2006},
}
Felix Finster, Niky Kamran, Joel Smoller, and Shing-Tung Yau. Decay of solutions of the wave equation in the Kerr geometry. 2006. Vol. 264. In Communications in Mathematical Physics. pp.465-503. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203644260670067.
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