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An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry

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arxiv gr-qc/0310024 v5 pith:V7VXXTLA submitted 2003-10-04 gr-qc astro-phmath-phmath.MP

Felix Finster , Niky Kamran , Joel Smoller , Shing-Tung Yau This is my paper · ORCID
classification gr-qcastro-phmath-phmath.MP
keywords geometryintegralkerrrepresentationequationodesscalarsolutions
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We consider the scalar wave equation in the Kerr geometry for Cauchy data which is smooth and compactly supported outside the event horizon. We derive an integral representation which expresses the solution as a superposition of solutions of the radial and angular ODEs which arise in the separation of variables. In particular, we prove completeness of the solutions of the separated ODEs. This integral representation is a suitable starting point for a detailed analysis of the long-time dynamics of scalar waves in the Kerr geometry.

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  1. 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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