From 2D Integrable Systems to Self-Dual Gravity

Journal article

We explain how to construct solutions to the self-dual Einstein vacuum equations from solutions of various two-dimensional integrable systems by exploiting the fact that the Lax formulations of both systems can be embedded in that of the self-dual Yang--Mills equations. We illustrate this by constructing explicit self-dual vacuum metrics on $\R^2\times \Sigma$, where $\Sigma$ is a homogeneous space for a real subgroup of $SL(2, \C)$ associated with the two-dimensional system.

Authors: Dunajski, M; Mason, L; Woodhouse, N

• Journal: J.Phys.A: Math.Gen
• Volume: 31
• Pages: 6019-6028
• Publication date: 1998-09-01
• DOI: 10.1088/0305-4470/31/28/015
• Keywords: nlin.SI; solv-int