Perturbations of an extremal Kerr spacetime: Analytic framework and late-time tails

2018/01/31 by Marc Casals, Peter Zimmerman · 13 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Event horizon #Formalism (music) #Geometry #Gravitation #Horizon #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Pulsars and Gravitational Waves Research #Quantum electrodynamics #Quantum mechanics #Scalar (mathematics) #Scalar field #Space time #Spacetime #Time domain #gr-qc #hep-th #math-ph #math.MP

paper · pdf · doi:10.1103/physrevd.100.124027

published in Physical review. D/Physical review. D. 100(12) (American Physical Society) · 34 pages, 1 figure; in v3: version matching the published version

openalex publication_date 2019/12/10 · arxiv created 2020/02/28 · arxiv updated 2020/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We develop a complete and systematic analytical approach to field perturbations of extremal Kerr spacetime based on the formalism of Mano, Suzuki, and Takasugi (MST) for the Teukolsky equation. Analytical expressions for the radial solutions and frequency-domain Green function in terms of infinite series of special functions are presented. As an application, we compute the leading late-time behavior due to the branch point at zero frequency of scalar, gravitational, and electromagnetic field perturbations on and off the event horizon. We also use the MST method to compute the leading behavior of the Green function modes near the branch point at the superradiant bound frequency and show that this behavior agrees with existing results in the literature using a different method.

Citations

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