Kerr stability in external regions
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913315218784256 |
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| author | Shen, Dawei |
| author_facet | Shen, Dawei |
| contents | 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}. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_12758 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Kerr stability in external regions Shen, Dawei Analysis of PDEs General Relativity and Quantum Cosmology Differential Geometry 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}. |
| title | Kerr stability in external regions |
| topic | Analysis of PDEs General Relativity and Quantum Cosmology Differential Geometry |
| url | https://arxiv.org/abs/2303.12758 |