English

From 2D Integrable Systems to Self-Dual Gravity

solv-int 2009-10-31 v1 Exactly Solvable and Integrable Systems

Abstract

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 R2×Σ\R^2\times \Sigma, where Σ\Sigma is a homogeneous space for a real subgroup of SL(2,\C)SL(2, \C) associated with the two-dimensional system.

Keywords

Cite

@article{arxiv.solv-int/9809006,
  title  = {From 2D Integrable Systems to Self-Dual Gravity},
  author = {M. Dunajski and L. J. Mason and N. M. J. Woodhouse},
  journal= {arXiv preprint arXiv:solv-int/9809006},
  year   = {2009}
}

Comments

9 pages, LaTex, no figures