Heavenly equations in de Sitter space

Abstract

A bstract 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 → 0.