Mode Stability of Hermitian Instantons
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 s...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2025 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2025
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/213194 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Mode Stability of Hermitian Instantons. Lars Andersson, Bernardo Araneda and Mattias Dahl. SIGMA 21 (2025), 022, 13 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862713593684819968 |
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| author | Andersson, Lars Araneda, Bernardo Dahl, Mattias |
| author_facet | Andersson, Lars Araneda, Bernardo Dahl, Mattias |
| citation_txt | Mode Stability of Hermitian Instantons. Lars Andersson, Bernardo Araneda and Mattias Dahl. SIGMA 21 (2025), 022, 13 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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 with variational instabilities.
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| first_indexed | 2026-03-19T22:18:32Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-213194 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-19T22:18:32Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Andersson, Lars Araneda, Bernardo Dahl, Mattias 2026-02-16T16:38:16Z 2025 Mode Stability of Hermitian Instantons. Lars Andersson, Bernardo Araneda and Mattias Dahl. SIGMA 21 (2025), 022, 13 pages 1815-0659 2020 Mathematics Subject Classification: 83C60; 53C25; 32Q26 arXiv:2410.21210 https://nasplib.isofts.kiev.ua/handle/123456789/213194 https://doi.org/10.3842/SIGMA.2025.022 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 with variational instabilities. This work was initiated while the authors were participating in the conference “Einstein Spaces and Special Geometry” at Institut Mittag-Leffler in Djursholm, Sweden, in July 2023. BA acknowledges support of the Institut Henri Poincaré (UAR 839 CNRS-Sorbonne Université) and LabEx CARMIN (ANR-10-LABX-59-01) in Paris, during a research stay. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Mode Stability of Hermitian Instantons Article published earlier |
| spellingShingle | Mode Stability of Hermitian Instantons Andersson, Lars Araneda, Bernardo Dahl, Mattias |
| title | Mode Stability of Hermitian Instantons |
| title_full | Mode Stability of Hermitian Instantons |
| title_fullStr | Mode Stability of Hermitian Instantons |
| title_full_unstemmed | Mode Stability of Hermitian Instantons |
| title_short | Mode Stability of Hermitian Instantons |
| title_sort | mode stability of hermitian instantons |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/213194 |
| work_keys_str_mv | AT anderssonlars modestabilityofhermitianinstantons AT aranedabernardo modestabilityofhermitianinstantons AT dahlmattias modestabilityofhermitianinstantons |