Self-dual gravity via Hitchin's equations

Abstract

In this work half-flat metrics are obtained from Hitchin's equations. The SU$(\infty )$ Hitchin's equations are obtained and as a consequence of them, the Husain-Park equation is found. Considering that the gauge group is SU$(2)$, some solutions associated to Liouville, sinh-Gordon and Painlevé III equations are taken and, through Moyal deformations, solutions of the SU$(\infty )$ Hitchin's equations are obtained. From these solutions, hamiltonian vector fields are determined, which in turn are used to construct the half-flat metrics. Following an approach of Dunajski, Mason and Woodhouse, it is also possible to construct half-flat metrics on $\mathcal{M}\times {\mathbb{CP}}^1$.

arXiv comment27+1 pages, no figures

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Cited by in corpus (1)

• New heavenly double copies