Precise asymptotics of the spin $+2$ Teukolsky field in the Kerr black hole interior
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915334255017984 |
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| author | Gurriaran, Sebastian |
| author_facet | Gurriaran, Sebastian |
| contents | Using a purely physical-space analysis, we prove the precise oscillatory blow-up asymptotics of the spin $+2$ Teukolsky field in the interior of a subextremal Kerr black hole. In particular, this work gives a new proof of the blueshift instability of the Kerr Cauchy horizon against linearized gravitational perturbations that was first shown by Sbierski \cite{sbierski}. In that sense, this work supports the Strong Cosmic Censorship conjecture in Kerr spacetimes. The proof is an extension to the Teukolsky equation of the work \cite{scalarMZ} by Ma and Zhang that treats the scalar wave equation in the interior of Kerr. The analysis relies on the generic polynomial decay on the event horizon of solutions of the Teukolsky equation that arise from compactly supported initial data, as recently proved by Ma and Zhang \cite{pricelaw} and Millet \cite{millet} in subextremal Kerr. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02670 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Precise asymptotics of the spin $+2$ Teukolsky field in the Kerr black hole interior Gurriaran, Sebastian General Relativity and Quantum Cosmology Analysis of PDEs 35Q75, 58J37, 58J45, 58K55, 83C57, 83C75 Using a purely physical-space analysis, we prove the precise oscillatory blow-up asymptotics of the spin $+2$ Teukolsky field in the interior of a subextremal Kerr black hole. In particular, this work gives a new proof of the blueshift instability of the Kerr Cauchy horizon against linearized gravitational perturbations that was first shown by Sbierski \cite{sbierski}. In that sense, this work supports the Strong Cosmic Censorship conjecture in Kerr spacetimes. The proof is an extension to the Teukolsky equation of the work \cite{scalarMZ} by Ma and Zhang that treats the scalar wave equation in the interior of Kerr. The analysis relies on the generic polynomial decay on the event horizon of solutions of the Teukolsky equation that arise from compactly supported initial data, as recently proved by Ma and Zhang \cite{pricelaw} and Millet \cite{millet} in subextremal Kerr. |
| title | Precise asymptotics of the spin $+2$ Teukolsky field in the Kerr black hole interior |
| topic | General Relativity and Quantum Cosmology Analysis of PDEs 35Q75, 58J37, 58J45, 58K55, 83C57, 83C75 |
| url | https://arxiv.org/abs/2409.02670 |