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Hidden symmetries of generalised gravitational instantons
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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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Cited by 1 Pith paper
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Incidence Relations for Self-Dual Black Holes
Closed-form deformed incidence relations are constructed for Eguchi-Hanson, self-dual Taub-NUT, and self-dual Plebanski-Demianski spacetimes by resumming the Dunajski-Mason recursion in Plebanski coordinates.
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