dorsal/arxiv
View SchemaFrom 2D Integrable Systems to Self-Dual Gravity
| Authors | M. Dunajski, L. J. Mason, N. M. J. Woodhouse |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9809006 |
| URL | https://arxiv.org/abs/solv-int/9809006 |
| DOI | 10.1088/0305-4470/31/28/015 |
| Journal | J.Phys.A: Math.Gen 31 (1998) 6019-6028 |
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 $\R^2\times \Sigma$, where $\Sigma$ is a homogeneous space for a real subgroup of $SL(2, \C)$ associated with the two-dimensional system.
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"abstract": "We explain how to construct solutions to the self-dual Einstein vacuum\nequations from solutions of various two-dimensional integrable systems by\nexploiting the fact that the Lax formulations of both systems can be embedded\nin that of the self-dual Yang--Mills equations. We illustrate this by\nconstructing explicit self-dual vacuum metrics on $\\R^2\\times \\Sigma$, where\n$\\Sigma$ is a homogeneous space for a real subgroup of $SL(2, \\C)$ associated\nwith the two-dimensional system.",
"arxiv_id": "solv-int/9809006",
"authors": [
"M. Dunajski",
"L. J. Mason",
"N. M. J. Woodhouse"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1088/0305-4470/31/28/015",
"journal_ref": "J.Phys.A: Math.Gen 31 (1998) 6019-6028",
"title": "From 2D Integrable Systems to Self-Dual Gravity",
"url": "https://arxiv.org/abs/solv-int/9809006"
},
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