Hidden symmetries of generalised gravitational instantons
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909381039226880 |
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| author | Araneda, Bernardo |
| author_facet | Araneda, Bernardo |
| contents | For conformally Kähler Riemannian four-manifolds with a Killing field, we present a framework to solve the field equations for generalised gravitational instantons corresponding to conformal self-duality and to cosmological Einstein-Maxwell. After deriving generic identities for the curvature of such manifolds without assuming field equations, we obtain $SU(\infty)$ Toda formulations for the Page-Pope, Plebanski-Demianski, and Chen-Teo classes, we show how to solve the (modified) Toda equation, and we use this to find conformally self-dual and Einstein-Maxwell generalisations of these geometries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05617 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hidden symmetries of generalised gravitational instantons Araneda, Bernardo General Relativity and Quantum Cosmology High Energy Physics - Theory Differential Geometry For conformally Kähler Riemannian four-manifolds with a Killing field, we present a framework to solve the field equations for generalised gravitational instantons corresponding to conformal self-duality and to cosmological Einstein-Maxwell. After deriving generic identities for the curvature of such manifolds without assuming field equations, we obtain $SU(\infty)$ Toda formulations for the Page-Pope, Plebanski-Demianski, and Chen-Teo classes, we show how to solve the (modified) Toda equation, and we use this to find conformally self-dual and Einstein-Maxwell generalisations of these geometries. |
| title | Hidden symmetries of generalised gravitational instantons |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Differential Geometry |
| url | https://arxiv.org/abs/2309.05617 |