Kerr stability in external regions
Abstract
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}.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2023
- DOI:
- 10.48550/arXiv.2303.12758
- arXiv:
- arXiv:2303.12758
- Bibcode:
- 2023arXiv230312758S
- Keywords:
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- Mathematics - Analysis of PDEs;
- General Relativity and Quantum Cosmology;
- Mathematics - Differential Geometry
- E-Print:
- 119 pages, 7 figures, accepted in Annals of PDE