Heavenly equations in de Sitter space

Abstract

We demonstrate that all anti-self-dual Einstein metrics with non--zero cosmological constant $\Lambda$ 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 $\Lambda \to 0$.

In memory of Jerzy Lukierski. A connection with the Chudecki-Przanowski equation and some other gauge choices clarified. Equation (3.5) corrected. Final version, to appear inn JHEP