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arXiv · 2606.14572

Heavenly equations in de Sitter space

Maciej Dunajski·Timothy Moy
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Abstract

We demonstrate that all anti-self-dual Einstein metrics with non--zero cosmological constant $Λ$ locally arise from solutions of a single second order PDE introduced by Lipstein and Nagy. We show how this equation fits into the heavenly formalism of Plebański, and establish a Lax pair. Finally we show how Plebański's second heavenly equation arises in the limit as $Λ\rightarrow 0$.

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Maciej Dunajski, Timothy Moy. 2026-08-24. Heavenly equations in de Sitter space. https://arxiv.org/abs/2606.14572

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