Mode Stability of Hermitian Instantons
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910900057800704 |
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| author | Andersson, Lars Araneda, Bernardo Dahl, Mattias |
| author_facet | Andersson, Lars Araneda, Bernardo Dahl, Mattias |
| contents | In this note, we prove the Riemannian analog of black hole mode stability for Hermitian, non-self-dual gravitational instantons which are either asymptotically locally flat (ALF) and Ricci-flat, or compact and Einstein with positive cosmological constant. We show that the Teukolsky equation on any such manifold is a positive definite operator. We also discuss the compatibility of the results with the existence of negative modes associated to variational instabilities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_21210 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mode Stability of Hermitian Instantons Andersson, Lars Araneda, Bernardo Dahl, Mattias General Relativity and Quantum Cosmology Differential Geometry In this note, we prove the Riemannian analog of black hole mode stability for Hermitian, non-self-dual gravitational instantons which are either asymptotically locally flat (ALF) and Ricci-flat, or compact and Einstein with positive cosmological constant. We show that the Teukolsky equation on any such manifold is a positive definite operator. We also discuss the compatibility of the results with the existence of negative modes associated to variational instabilities. |
| title | Mode Stability of Hermitian Instantons |
| topic | General Relativity and Quantum Cosmology Differential Geometry |
| url | https://arxiv.org/abs/2410.21210 |