Teukolsky equations, twistor functions, and conformally self-dual spaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910527896158208 |
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| author | Araneda, Bernardo |
| author_facet | Araneda, Bernardo |
| contents | We prove a correspondence, for Riemannian manifolds with self-dual Weyl tensor, between twistor functions and solutions to the Teukolsky equations for any conformal and spin weights. In particular, we give a contour integral formula for solutions to the Teukolsky equations, and we find a recursion operator that generates an infinite family of solutions and leads to the construction of Cech representatives and sheaf cohomology classes on twistor space. Apart from the general conformally self-dual case, examples include self-dual black holes, scalar-flat Kähler surfaces, and quaternionic-Kähler metrics, where we map the Teukolsky equation to the conformal wave equation, establish new relations to the linearised Przanowski equation, and find new classes of quaternionic deformations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_10939 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Teukolsky equations, twistor functions, and conformally self-dual spaces Araneda, Bernardo General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics We prove a correspondence, for Riemannian manifolds with self-dual Weyl tensor, between twistor functions and solutions to the Teukolsky equations for any conformal and spin weights. In particular, we give a contour integral formula for solutions to the Teukolsky equations, and we find a recursion operator that generates an infinite family of solutions and leads to the construction of Cech representatives and sheaf cohomology classes on twistor space. Apart from the general conformally self-dual case, examples include self-dual black holes, scalar-flat Kähler surfaces, and quaternionic-Kähler metrics, where we map the Teukolsky equation to the conformal wave equation, establish new relations to the linearised Przanowski equation, and find new classes of quaternionic deformations. |
| title | Teukolsky equations, twistor functions, and conformally self-dual spaces |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2407.10939 |