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MiS Preprint

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


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.

Oct 28, 2003
Oct 28, 2003

Related publications

2005 Repository Open Access
Felix Finster, Niky Kamran, Joel Smoller and Shing-Tung Yau

An integral spectral representation of the propagator for the wave equation in the Kerr geometry

In: Communications in mathematical physics, 260 (2005) 2, pp. 257-298