Communications in Mathematical Physics

, Volume 264, Issue 2, pp 465–503

Decay of Solutions of the Wave Equation in the Kerr Geometry

Article

DOI: 10.1007/s00220-006-1525-8

Cite this article as:
Finster, F., Kamran, N., Smoller, J. et al. Commun. Math. Phys. (2006) 264: 465. doi:10.1007/s00220-006-1525-8

Abstract

We consider the Cauchy problem for the massless scalar wave equation in the Kerr geometry for smooth initial data compactly supported outside the event horizon. We prove that the solutions decay in time in Lloc. The proof is based on a representation of the solution as an infinite sum over the angular momentum modes, each of which is an integral of the energy variable ω on the real line. This integral representation involves solutions of the radial and angular ODEs which arise in the separation of variables.

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

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