Exponentially-growing Mode Instability on Reissner-Nordström--Anti-de-Sitter black holes
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866918504678031360 |
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| author | Zheng, Weihao |
| author_facet | Zheng, Weihao |
| contents | We construct growing mode solutions to the uncharged and charged Klein-Gordon equations on the sub-extremal Reissner-Nordström--anti-de-Sitter (AdS) spacetime under reflecting (Dirichlet or Neumann) boundary conditions. Our result applies to a range of Klein-Gordon masses above the so-called Breitenlohner-Freedman bound, notably including the conformal mass case. The mode instability of the Reissner-Nordström--AdS spacetime for some black hole parameters is in sharp contrast to the Schwarzschild-AdS spacetime, where the solution to the Klein-Gordon equation is known to decay in time. Contrary to other mode instability results on the Kerr and Kerr-AdS spacetimes, our growing mode solutions of the uncharged and weakly charged Klein-Gordon equation exist independently of the occurrence or absence of superradiance. We discover a novel mechanism leading to a growing mode solution, namely, a near-extremal instability for the Klein-Gordon equation. Our result seems to be the first rigorous mathematical realization of this instability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04750 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exponentially-growing Mode Instability on Reissner-Nordström--Anti-de-Sitter black holes Zheng, Weihao General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs We construct growing mode solutions to the uncharged and charged Klein-Gordon equations on the sub-extremal Reissner-Nordström--anti-de-Sitter (AdS) spacetime under reflecting (Dirichlet or Neumann) boundary conditions. Our result applies to a range of Klein-Gordon masses above the so-called Breitenlohner-Freedman bound, notably including the conformal mass case. The mode instability of the Reissner-Nordström--AdS spacetime for some black hole parameters is in sharp contrast to the Schwarzschild-AdS spacetime, where the solution to the Klein-Gordon equation is known to decay in time. Contrary to other mode instability results on the Kerr and Kerr-AdS spacetimes, our growing mode solutions of the uncharged and weakly charged Klein-Gordon equation exist independently of the occurrence or absence of superradiance. We discover a novel mechanism leading to a growing mode solution, namely, a near-extremal instability for the Klein-Gordon equation. Our result seems to be the first rigorous mathematical realization of this instability. |
| title | Exponentially-growing Mode Instability on Reissner-Nordström--Anti-de-Sitter black holes |
| topic | General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2410.04750 |