, Volume 264, Issue 2, pp 465-503
Date: 01 Mar 2006

Decay of Solutions of the Wave Equation in the Kerr Geometry

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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 L loc. 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.

Communicated by G.W. Gibbons
Research supported in part by the Deutsche Forschungsgemeinschaft.
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.
An erratum to this article is available at http://dx.doi.org/10.1007/s00220-008-0458-9.