Decay of Solutions of the Wave Equation in the Kerr Geometry
Felix Finster, Niky Kamran, Joel Smoller, and Shing-Tung Yau
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Submission date: 19. Apr. 2005
published in: Communications in mathematical physics, 264 (2006) 2, p. 465-503
DOI number (of the published article): 10.1007/s00220-006-1525-8
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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 . 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.