# The non-autonomous chiral model and the Ernst equation of General Relativity in the bidifferential calculus framework

@article{Dimakis2011TheNC, title={The non-autonomous chiral model and the Ernst equation of General Relativity in the bidifferential calculus framework}, author={Aristophanes Dimakis and Nils Kanning and Folkert Muller-Hoissen}, journal={Symmetry Integrability and Geometry-methods and Applications}, year={2011}, volume={7}, pages={118} }

The non-autonomous chiral model equation for an m m matrix function on a two-dimensional space appears in particular in general relativity, where for m = 2 a certain reduction of it determines stationary, axially symmetric solutions of Einstein's vacuum equations, and for m = 3 solutions of the Einstein{Maxwell equations. Using a very simple and general result of the bidifferential calculus approach to integrable partial differential and difference equations, we generate a large class of exact…

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