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The non-autonomous chiral model equation for an $m \times m$ matrix functionon a two-dimensional space appears in particular in general relativity, wherefor $m=2$ a certain reduction of it determines stationary, axially symmetricsolutions of Einstein's vacuum equations, and for $m=3$ solutions of theEinstein-Maxwell equations. Using a very simple and general result of thebidifferential calculus approach to integrable partial differential anddifference equations, we generate a large class of exact solutions of thischiral model. The solutions are parametrized by a set of matrices, the size ofwhich can be arbitrarily large. The matrices are subject to a Sylvesterequation that has to be solved and generically admits a unique solution. Byimposing the aforementioned reductions on the matrix data, we recover the Ernstpotentials of multi-Kerr-NUT and multi-Demianski-Newman metrics.

The Non-Autonomous Chiral Model and the Ernst Equation of General Relativity in the Bidifferential Calculus Framework