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

URN to cite this document:: urn:nbn:de:bvb:355-epub-110008
DOI to cite this document:: 10.5283/epub.11000

Finster, Felix ; Kamran, Niky ; Smoller, J. ; Yau, S.-T.

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Date of publication of this fulltext: 27 Nov 2009 07:13

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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 ...