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An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry

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Abstract

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.

This integral representation is a suitable starting point for a detailed analysis of the long-time dynamics of scalar waves in the Kerr geometry.

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Authors and Affiliations

  1. NWF I – Mathematik, Universität Regensburg, 93040, Regensburg, Germany

    F. Finster

  2. Department of Math. and Statistics, McGill University, Montréal, Québec, Canada, H3A 2K6

    N. Kamran

  3. Mathematics Department, The University of Michigan, Ann Arbor, MI, 48109, USA

    J. Smoller

  4. Mathematics Department, Harvard University, Cambridge, MA, 02138, USA

    S.-T. Yau

Authors
  1. F. Finster
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  2. N. Kamran
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  3. J. Smoller
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  4. S.-T. Yau
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Corresponding author

Correspondence to F. Finster.

Additional information

Communicated by G.W. Gibbons

Research supported by NSERC grant # RGPIN 105490-2004.

Research supported in part by the NSF, Grant No. DMS-010-3998.

Research supported in part by the NSF, Grant No. 33-585-7510-2-30.

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Finster, F., Kamran, N., Smoller, J. et al. An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry. Commun. Math. Phys. 260, 257–298 (2005). https://doi.org/10.1007/s00220-005-1390-x

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  • DOI: https://doi.org/10.1007/s00220-005-1390-x

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