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Decay of Solutions of the Wave Equation in the Kerr Geometry

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arxiv gr-qc/0504047 v5 pith:M5THGAIJ submitted 2005-04-12 gr-qc math-phmath.MP

Felix Finster , Niky Kamran , Joel Smoller , Shing-Tung Yau This is my paper · ORCID
classification gr-qcmath-phmath.MP
keywords solutionsangulardecayequationgeometryintegralkerrrepresentation
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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 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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 134 citations worldwide. Full citation record

  1. Threshold-Sharp Conformal Scalar Stability on Carter Slabs and Black Hole Exteriors

    math.AP 2026-05 unverdicted novelty 5.0 of 10

    Proves threshold-sharp stability for the conformal scalar-curvature sector on Carter slabs and extends the framework to black hole exteriors like Kerr and Reissner-Nordström.

  2. On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes

    gr-qc 2025-07 conditional novelty 4.0 of 10

    For subextremal Kerr spacetimes, the paper constructs a positive-definite, conserved Hamiltonian energy for axially symmetric linear perturbations, indicating a form of linear stability within this symmetry class.

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