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

Felix Finster, Niky Kamran, Joel Smoller, and Shing-Tung Yau

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Submission date: 28. Oct. 2003
Pages: 42
published in: Communications in mathematical physics, 260 (2005) 2, p. 257-298 
DOI number (of the published article): 10.1007/s00220-005-1390-x
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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.