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

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arxiv 2007.07211 v2 pith:WPODWMPM submitted 2020-07-14 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 equationkerrteukolskyfullsubextremaldecayestimatesfrequency
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abstract

This paper is the first of a series regarding the Teukolsky equation of spin $\pm 1$ and spin $\pm 2$ on Kerr backgrounds in the full subextremal range of parameters $|a|<M$. In the present paper, we study fixed frequency solutions of the transformed system of equations introduced by Dafermos, Holzegel and Rodnianski, obtaining estimates which are uniform in the separation parameters. A corollary of our result, to be laid out in the second paper of the series, is that solutions of the Teukolsky equation on subextremal Kerr arising from regular initial data remain bounded and decay in time. This is a key step in establishing the full linear stability of Kerr under electromagnetic and gravitational perturbations. Our estimates can also be applied to understanding more delicate features of the Teukolsky equation, such as their scattering properties.

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Cited by 6 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. Hidden Symmetry of Kerr-deSitter from Manifest Symmetry of Painlev\'e VI

    gr-qc 2026-08 conditional novelty 6.0 of 10

    Mass symmetries of the Kerr-deSitter Teukolsky equation are shown to follow from a symmetry of Painlevé VI via isomonodromy, and the dual spacetime is a black hole whose horizon angular velocities give a known mode-st...

  6. Teukolsky on slowly-rotating Kerr-de Sitter in the vanishing $\Lambda$ limit

    math.AP 2026-01 accept novelty 6.0 of 10

    Energy, Morawetz and r^p-weighted estimates are proved for Teukolsky equations on slowly-rotating Kerr-de Sitter, uniformly as the cosmological constant tends to zero, recovering known Kerr-Teukolsky estimates in the limit.

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