Teukolsky equations in perturbations of Kerr
Abstract
The Kerr stability conjecture has been proved in the slowly rotating case, i.e., |a|≪ m, in the sequence of works \cite{KS-GCM1} \cite{KS-GCM2} \cite{KS:Kerr} by Sergiu Klainerman and the author, \cite{GKS22} by Elena Giorgi, Sergiu Klainerman and the author, and \cite{Shen} by Dawei Shen, and extended in \cite{Sze}, by the author, to the full subextremal range |a|<m, thereby completing the proof of the Kerr stability conjecture. The proof in \cite{Sze} crucially relies on the two companion papers \cite{MaSz24} \cite{MaSz26} by Siyuan Ma and the author, in which we prove energy-Morawetz estimates respectively for the scalar wave equation and for Teukolsky equations on perturbations of Kerr with |a|<m. In addition, two results in \cite{Sze}, concerning the derivation of the Teukolsky wave-transport system in perturbations of Kerr and energy-Morawetz estimates for Teukolsky in the setting of \cite{Sze}, are stated without proofs. The goal of the present paper companion paper to \cite{Sze} is to provide the proof of these two results.
Related
- Teukolsky Master Equation for a Kerr-like metric with Mass Quadrupole Moment
- Perturbations of Kerr-Newman black holes: separation and mode stability
- Separation of variables for coupled radiative perturbations of Kerr-Newman-de Sitter black holes
- Admissible characterization in delay equations and robustness of exponential dichotomies against small-delay perturbations
- Generalized Whiting transform and Flux Estimates for Wave Equations in Subextremal Kerr
BibTeX
@misc{szeftel2026teukolsky,
title = {{Teukolsky equations in perturbations of Kerr}},
author = {Jérémie Szeftel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.40315},
eprint = {2609.40315},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40315},
}
RIS
TY - UNPB
TI - Teukolsky equations in perturbations of Kerr
AU - Jérémie Szeftel
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.40315
UR - https://arxiv.org/abs/2609.40315
AB - The Kerr stability conjecture has been proved in the slowly rotating case, i.e., |a|≪ m, in the sequence of works \cite{KS-GCM1} \cite{KS-GCM2} \cite{KS:Kerr} by Sergiu Klainerman and the author, \cite{GKS22} by Elena Giorgi, Sergiu Klainerman and the author, and \cite{Shen} by Dawei Shen, and extended in \cite{Sze}, by the author, to the full subextremal range |a|<m, thereby completing the proof of the Kerr stability conjecture. The proof in \cite{Sze} crucially relies on the two companion papers \cite{MaSz24} \cite{MaSz26} by Siyuan Ma and the author, in which we prove energy-Morawetz estimates respectively for the scalar wave equation and for Teukolsky equations on perturbations of Kerr with |a|<m. In addition, two results in \cite{Sze}, concerning the derivation of the Teukolsky wave-transport system in perturbations of Kerr and energy-Morawetz estimates for Teukolsky in the setting of \cite{Sze}, are stated without proofs. The goal of the present paper companion paper to \cite{Sze} is to provide the proof of these two results.
ER -