The dual twistor theory of self-dual black holes
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918278221266944 |
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| author | Adamo, Tim Araneda, Bernardo Seet, Sean |
| author_facet | Adamo, Tim Araneda, Bernardo Seet, Sean |
| contents | The Taub-NUT and Eguchi-Hanson gravitational instantons, along with the self-dual Plebanski-Demianski metric, form a set of Euclidean metrics which can naturally be called `self-dual black holes', as they arise from self-dual slices of the most general vacuum, asymptotically flat black hole metric. These self-dual black holes are of interest for many reasons, and can famously be described through the non-linear graviton construction of twistor theory. However, the implicit nature of this twistor description obscures some features of the underlying geometry, particularly for the most general self-dual black holes. In this paper, we give a new construction of all asymptotically flat self-dual black holes based on holomorphic quadrics in flat dual twistor space, rather than the usual twistor space associated with self-duality. Remarkably, the geometry of the self-dual black holes -- including their hyperkahler structure, as well as Kerr-Schild and Gibbons-Hawking forms -- is directly encoded in the corresponding quadric. As a consequence, we obtain a previously unknown single Kerr-Schild form of the self-dual Plebanski-Demianski metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05037 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The dual twistor theory of self-dual black holes Adamo, Tim Araneda, Bernardo Seet, Sean High Energy Physics - Theory General Relativity and Quantum Cosmology Differential Geometry The Taub-NUT and Eguchi-Hanson gravitational instantons, along with the self-dual Plebanski-Demianski metric, form a set of Euclidean metrics which can naturally be called `self-dual black holes', as they arise from self-dual slices of the most general vacuum, asymptotically flat black hole metric. These self-dual black holes are of interest for many reasons, and can famously be described through the non-linear graviton construction of twistor theory. However, the implicit nature of this twistor description obscures some features of the underlying geometry, particularly for the most general self-dual black holes. In this paper, we give a new construction of all asymptotically flat self-dual black holes based on holomorphic quadrics in flat dual twistor space, rather than the usual twistor space associated with self-duality. Remarkably, the geometry of the self-dual black holes -- including their hyperkahler structure, as well as Kerr-Schild and Gibbons-Hawking forms -- is directly encoded in the corresponding quadric. As a consequence, we obtain a previously unknown single Kerr-Schild form of the self-dual Plebanski-Demianski metric. |
| title | The dual twistor theory of self-dual black holes |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Differential Geometry |
| url | https://arxiv.org/abs/2601.05037 |