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

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

2003-10-04

arxiv.org/abs/gr-qc/0310024v5

Commun.Math.Phys. 260 (2005) 257-298

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

41 pages, 4 figures, minor corrections

Scientific paper

10.1007/s00220-005-1390-x

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.

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