Decay of Solutions of the Wave Equation in the Kerr Geometry

Abstract

We consider the Cauchy problem for the scalar wave equation in the Kerr geometry for smooth initial data supported outside the event horizon. We prove that the solutions decay in time in L^\infty_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 on the real line. This integral representation involves solutions of the radial and angular ODEs which arise in the separation of variables.

44 pages, 5 figures, minor corrections

References in corpus (4)

• Superradiant instabilities of rotating black branes and strings
• The Long-Time Dynamics of Dirac Particles in the Kerr-Newman Black Hole Geometry
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• Spectral Estimates and Non-Selfadjoint Perturbations of Spheroidal Wave Operators

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