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Article Dans Une Revue Ann.PDE Année : 2024

Kerr stability in external regions

Résumé

In 2003, Klainerman and Nicolò\cite{Kl-Ni} proved the stability of Minkowski in the case of the exterior of an outgoing null cone. Relying on the method used in \cite{Kl-Ni}, Caciotta and Nicolò\cite{Ca-Ni} proved the stability of Kerr spacetime in external regions, i.e. outside an outgoing null cone far away from the Kerr event horizon. In this paper, we give a new proof of \cite{Ca-Ni}. Compared to \cite{Ca-Ni}, we reduce the number of derivatives needed in the proof, simplify the treatment of the last slice, and provide a unified treatment of the decay of initial data which contains in particular the initial data considered by Klainerman and Szeftel in \cite{KS:main}. Also, concerning the treatment of curvature estimates, similar to \cite{ShenMink}, we replace the vectorfield method used in \cite{Kl-Ni,Ca-Ni} by $r^p$-weighted estimates introduced by Dafermos and Rodnianski in \cite{Da-Ro}.

Dates et versions

hal-04060400 , version 1 (06-04-2023)

Identifiants

Citer

Dawei Shen. Kerr stability in external regions. Ann.PDE, 2024, 10 (1), pp.9. ⟨10.1007/s40818-024-00173-0⟩. ⟨hal-04060400⟩
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