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}.
Mots clés
Double null foliation
Geodesic foliation
Kerr stability
Linearization procedure
Peeling properties
rp\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$r^p$$\end{document}–weighted estimates