Communications in Mathematical Physics

, Volume 260, Issue 2, pp 257–298

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

Article

DOI: 10.1007/s00220-005-1390-x

Cite this article as:
Finster, F., Kamran, N., Smoller, J. et al. Commun. Math. Phys. (2005) 260: 257. doi:10.1007/s00220-005-1390-x

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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.NWF I – MathematikUniversität RegensburgRegensburgGermany
  2. 2.Department of Math. and StatisticsMcGill UniversityMontréalCanada
  3. 3.Mathematics DepartmentThe University of MichiganAnn ArborUSA
  4. 4.Mathematics DepartmentHarvard UniversityCambridgeUSA