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This article is cited in 2 scientific papers (total in 2 papers)
The Non-Autonomous Chiral Model and the Ernst Equation of General Relativity in the Bidifferential Calculus Framework
Aristophanes Dimakisa, Nils Kanningb, Folkert Müller-Hoissenc a Department of Financial and Management Engineering, University of the Aegean, 41, Kountourioti Str., 82100 Chios, Greece
b Institute for Mathematics and Institute for Physics, Humboldt University, Rudower Chaussee 25, 12489 Berlin, Germany
c Max-Planck-Institute for Dynamics and Self-Organization, Bunsenstrasse 10, 37073 Göttingen, Germany
Abstract:
The non-autonomous chiral model equation for an $m\times m$ 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 solutions of this chiral model. The solutions are parametrized by a set of matrices, the size of which can be arbitrarily large. The matrices are subject to a Sylvester equation that has to be solved and generically admits a unique solution.
By imposing the aforementioned reductions on the matrix data, we recover the Ernst potentials of multi-Kerr-NUT and multi-Demiański–Newman metrics.
Keywords:
bidifferential calculus, chiral model, Ernst equation, Sylvester equation.
Received: August 31, 2011; in final form December 16, 2011; Published online December 23, 2011
Citation:
Aristophanes Dimakis, Nils Kanning, Folkert Müller-Hoissen, “The Non-Autonomous Chiral Model and the Ernst Equation of General Relativity in the Bidifferential Calculus Framework”, SIGMA, 7 (2011), 118, 27 pp.
Linking options:
https://www.mathnet.ru/eng/sigma676 https://www.mathnet.ru/eng/sigma/v7/p118
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