From 2D Integrable Systems to Self-Dual Gravity

Details From 2D Integrable Systems to Self-Dual Gravity From 2D Integrable Systems to Self-Dual Gravity

1998-08-31

arxiv.org/abs/solv-int/9809006v1

J.Phys.A: Math.Gen 31 (1998) 6019-6028

Nonlinear Sciences

Exactly Solvable and Integrable Systems

9 pages, LaTex, no figures

Scientific paper

10.1088/0305-4470/31/28/015

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.

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