Finster, Felix and Kamran, Niky and Smoller, J. and Yau, S.-T. (2005) An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry. Communications in Mathematical Physics 260 (2), pp. 257-298.
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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.
|Institutions:||Mathematics > Prof. Dr. Felix Finster|
|Subjects:||500 Science > 510 Mathematics|
|Refereed:||Yes, this version has been refereed|
|Created at the University of Regensburg:||Yes|
|Deposited On:||27 Nov 2009 08:13|
|Last Modified:||08 Oct 2012 08:40|
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