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.

20 pages, latex, minor corrections

References in corpus (5)

• Harmonic space and quaternionic manifolds
• On Self-Dual Gravity I
• The matreoshka of supersymmetric self-dual theories
• Super Self-Duality as Analyticity in Harmonic Superspace
• From 2D conformal to 4D self-dual theories: quaternionic analyticity

Cited by in corpus (7)

• Self-Dual Supergravity and Twistor Theory
• SELF-DUAL SUPERGRAVITIES
• An action of N=8 self-dual supergravity in ultra-hyperbolic harmonic superspace
• Four Dimensional Integrable Theories
• On pseudo-hyperkähler prepotentials
• String-induced Yang-Mills coupling to self-dual gravity
• Unravelling the On-shell Constraints of Self-dual Supergravity Theories