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

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dc.contributor.author Dimakis, A.
dc.contributor.author Kanning, N.
dc.contributor.author Müller-Hoissen, F.
dc.date.accessioned 2019-02-16T20:47:24Z
dc.date.available 2019-02-16T20:47:24Z
dc.date.issued 2011
dc.identifier.citation The Non-Autonomous Chiral Model and the Ernst Equation of General Relativity in the Bidifferential Calculus Framework / A. Dimakis, N. Kanning, F. Müller-Hoissen // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 57 назв. — англ. uk_UA
dc.identifier.issn 1815-0659
dc.identifier.other 2010 Mathematics Subject Classification: 37K10; 16E45
dc.identifier.other DOI: http://dx.doi.org/10.3842/SIGMA.2011.118
dc.identifier.uri http://dspace.nbuv.gov.ua/handle/123456789/148083
dc.description.abstract 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 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-Deminski-Newman metrics. uk_UA
dc.description.sponsorship We would like to thank Vladimir S. Manko and anonymous referees for helpful comments. During the course of this work, N.K. has been at the Max-Planck-Institute for Dynamics and Self-Organization in G¨ottingen. uk_UA
dc.language.iso en uk_UA
dc.publisher Інститут математики НАН України uk_UA
dc.relation.ispartof Symmetry, Integrability and Geometry: Methods and Applications
dc.title The Non-Autonomous Chiral Model and the Ernst Equation of General Relativity in the Bidifferential Calculus Framework uk_UA
dc.type Article uk_UA
dc.status published earlier uk_UA


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