, Volume 260, Issue 2, pp 257-298

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.

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.