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arXiv · 2309.05617

Hidden symmetries of generalised gravitational instantons

Bernardo Araneda
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Abstract

For conformally K\"ahler 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.

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Bernardo Araneda. 2023-09-11. Hidden symmetries of generalised gravitational instantons. https://arxiv.org/abs/2309.05617

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