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Boundedness and decay for the Teukolsky equation on Kerr in the full subextremal range $|a|<M$: physical space analysis

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arxiv 2302.08916 v2 pith:V2LX274S submitted 2023-02-17 gr-qc math-phmath.APmath.DGmath.MP

Yakov Shlapentokh-Rothman , Rita Teixeira da Costa This is my paper · ORCID
classification gr-qcmath-phmath.APmath.DGmath.MP
keywords teukolskyequationestimateskerrsubextremalarxivdecayfull
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abstract

This paper concludes the study, initiated by the authors in arXiv:2007.07211, of the Teukolsky equation of spin $\pm 1$ and spin $\pm 2$ on Kerr backgrounds in the full subextremal range of parameters $|a| < M$. In our previous arXiv:2007.07211, we obtained uniform-in-frequency estimates for the ODEs governing separable solutions to the Teukolsky equation. In this paper, by adapting the techniques developed by the first author with Dafermos and Rodnianski for scalar waves, we show that our ODE estimates can be upgraded to estimates for the Teukolsky PDE. In particular, we conclude the proof that solutions of the Teukolsky equation on subextremal Kerr arising from regular initial data remain bounded and decay in time.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Linear stability of Kerr black holes in the full subextremal range

    gr-qc 2025-06 conditional novelty 8.0 of 10

    Proof that linearized perturbations of subextremal Kerr black holes decay to a linearized Kerr solution for the full range |a| < m.

  2. Elliptic curvature estimates for linearised gravitational perturbations of Kerr in the full sub-extremal range $|a|<M$

    gr-qc 2025-09 conditional novelty 7.0 of 10

    For all sub-extremal Kerr spacetimes |a|<M, angular elliptic estimates control the full linearised curvature by the extremal Teukolsky components up to lower-order terms.

  3. Conservation Laws and Boundedness for Linearised Einstein--Maxwell Equations on the Reissner--Nordstr\"om Black Hole

    gr-qc 2025-06 conditional novelty 7.0 of 10

    A canonical energy conservation law in double null gauge yields uniform boundedness of energy fluxes for the gauge-invariant Teukolsky variables of linearised Einstein-Maxwell perturbations of Reissner-Nordström for |...

  4. A Physical space derivation of Morawetz-Energy estimates in Kerr spacetimes with large angular momentum

    gr-qc 2026-07 conditional novelty 6.5 of 10

    Physical-space Morawetz-energy estimates hold for the scalar wave equation on Kerr with |a|/m ≤ 0.75, via trapping-set characterization, Stogin-type low-frequency control, and a physical-space Whiting transform.

  5. Ergodic Hysteresis of the Kerr black hole spectrum

    gr-qc 2025-11 conditional novelty 6.0 of 10

    Near-extremal Kerr black holes with massive scalar fields exhibit a cascade of exceptional points that can adiabatically permute arbitrary quasinormal-mode overtones.

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