Self-Dual Gravity Revisited

Abstract

Reconsidering the harmonic space description of the self-dual Einstein equations, we streamline the proof that all self-dual pure gravitational fields allow a local description in terms of an unconstrained analytic prepotential in harmonic space. Our formulation yields a simple recipe for constructing self-dual metrics starting from any explicit choice of such prepotential; and we illustrate the procedure by producing a metric related to the Taub-NUT solution from the simplest monomial choice of prepotential.