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 $\mathcal{M}\times {\mathbb{CP}}^1$.

27+1 pages, no figures

References in corpus (6)

• Black holes and the double copy
• The Kinematic Algebra From the Self-Dual Sector
• Integrable Background Geometries
• Octonions, Monopoles, and Knots
• Nonsingular solutions of Hitchin's equations for noncompact gauge groups
• Gravitational interpretation of the Hitchin equations