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A general formalism for the stability of Kerr

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arxiv 2002.02740 v1 pith:777HBCT6 submitted 2020-02-07 math.AP gr-qcmath-phmath.DGmath.MP

Elena Giorgi , Sergiu Klainerman , Jérémie Szeftel This is my paper · ORCID
classification math.APgr-qcmath-phmath.DGmath.MP
keywords kerrnonlinearcitesettingstabilityanalyzingchandrasekharcontains
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The goal of this paper is to provide a geometric framework for analyzing the uniform decay properties of solutions to the Teukolsky equation in the fully nonlinear setting of perturbations of Kerr. It contains the first nonlinear version of the Chandrasekhar transformation introduced in the linearized setting in \cite{D-H-R-Kerr} and \cite{Ma} with the intent to use it in our ongoing project to prove the full nonlinear stability of slowly rotating Kerr as solution to the Einstein vacuum equations.

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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. 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.

  2. On the uniqueness of Kerr-de Sitter spacetimes

    gr-qc 2025-09 conditional novelty 7.0 of 10

    Under compatibility conditions on both horizons, every smooth stationary vacuum solution with positive cosmological constant is claimed to be isometric to Kerr-de Sitter in its stationary region.

  3. On Kerr black hole formation with complete apparent horizon and a new approach toward Penrose inequality

    gr-qc 2025-05 conditional novelty 7.0 of 10

    The authors prove that scale-critical short-pulse initial data can produce global Kerr black hole formation spacetimes with a complete apparent horizon, and they derive dynamical and spacetime Penrose inequalities in ...

  4. 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.

  5. 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.

  6. 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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