Overdamped QNM for Schwarzschild black holes
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910948811341824 |
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| author | Hitrik, Michael Zworski, Maciej |
| author_facet | Hitrik, Michael Zworski, Maciej |
| contents | We prove that the number of quasinormal modes (QNM) for Schwarzschild and Schwarzschild-de Sitter black holes in a disc of radius $ r $ is bounded from below by $ c r^3 $. This shows that the recent upper bound by Jézéquel is sharp. The argument is an application of a spectral asymptotics result for non-self-adjoint operators which provides a finer description of QNM and explains the emergence of a distorted lattice on which they lie. Our presentation gives a general result about exponentially accurate Bohr-Sommerfeld quantization rules for one dimensional problems. The description of QNM allows their accurate evaluation ``deep in the complex" where numerical methods break down due to pseudospectral effects. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_15924 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Overdamped QNM for Schwarzschild black holes Hitrik, Michael Zworski, Maciej Mathematical Physics Spectral Theory We prove that the number of quasinormal modes (QNM) for Schwarzschild and Schwarzschild-de Sitter black holes in a disc of radius $ r $ is bounded from below by $ c r^3 $. This shows that the recent upper bound by Jézéquel is sharp. The argument is an application of a spectral asymptotics result for non-self-adjoint operators which provides a finer description of QNM and explains the emergence of a distorted lattice on which they lie. Our presentation gives a general result about exponentially accurate Bohr-Sommerfeld quantization rules for one dimensional problems. The description of QNM allows their accurate evaluation ``deep in the complex" where numerical methods break down due to pseudospectral effects. |
| title | Overdamped QNM for Schwarzschild black holes |
| topic | Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2406.15924 |