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Wave equations estimates and the nonlinear stability of slowly rotating Kerr black holes

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arxiv 2205.14808 v1 pith:F3LTLG6L submitted 2022-05-30 math.AP

Elena Giorgi , Sergiu Klainerman , Jeremie Szeftel This is my paper · ORCID
classification math.AP
keywords citekerrestimatesnonlinearproofstabilitycompletepart
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abstract

This is the last part of our proof of the nonlinear stability of the Kerr family for small angular momentum, i.e $|a|/m\ll 1$, in which we deal with the nonlinear wave type estimates needed to complete the project. More precisely we provide complete proofs for Theorems M1 and M2 as well the curvature estimates of Theorem M8, which were stated without proof in sections 3.7.1 and 9.4.7 of \cite{KS:Kerr}. Our procedure is based on a new general interest formalism (detailed in Part I of this work), which extends the one used in the stability of Minkowski space. Together with \cite{KS:Kerr} and the GCM papers \cite{KS-GCM1}, \cite{KS-GCM2}, \cite{Shen}, this work completes proof of the Main Theorem stated in Section 3.4 of \cite{KS:Kerr}.

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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. A canonical foliation on null infinity in perturbations of Kerr

    gr-qc 2024-12 conditional novelty 7.0 of 10

    A canonical LGCM foliation of future null infinity is constructed in perturbed Kerr spacetimes, giving unique definitions of energy, momentum, angular momentum and center of mass with standard radiation laws.

  3. Horizons of some asymptotically stationary spacetimes

    gr-qc 2024-11 conditional novelty 7.0 of 10

    Small time-decaying perturbations of stationary black hole spacetimes admit a unique smooth null horizon asymptotic to the unperturbed horizon, equal to the event horizon under global assumptions.

  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. 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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