Decay of Solutions of the Wave Equation in the Kerr Geometry

Details Decay of Solutions of the Wave Equation in the Kerr Geometry Decay of Solutions of the Wave Equation in the Kerr Geometry

2005-04-12

arxiv.org/abs/gr-qc/0504047v5

Commun.Math.Phys. 264 (2006) 465-503

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

44 pages, 5 figures, minor corrections

Scientific paper

10.1007/s00220-006-1525-8

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.

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