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arXiv · 1812.08962

Self-dual gravity via Hitchin's equations

Erick Chacon·Hugo Garcia-Compean
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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 ${\cal M} \times\mathbb{CP}^{1}$.

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Erick Chacon, Hugo Garcia-Compean. 2018-12-21. Self-dual gravity via Hitchin's equations. https://doi.org/10.1063/1.5088452

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