Heavenly equations in de Sitter space

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 hyper--heavenly formalism of Plebański, and establish a Lax pair. Finally we show how Plebański's second heavenly equation arises in the limit as $Λ\rightarrow 0$.