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

Dimakis, A., Kanning, N., & Müller-Hoissen, F. (2011). The non-autonomous chiral model and the Ernst equation of General Relativity in the bidifferential calculus framework. Symmetry, Integrability and Geometry: Methods and Applications, 7: 118. doi:10.3842/SIGMA.2011.118.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-113B-1 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-113C-0
Genre: Journal Article

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 Creators:
Dimakis, Aristophanes, Author
Kanning, Nils1, Author              
Müller-Hoissen, Folkert1, Author              
Affiliations:
1Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063285              

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Free keywords: bidifferential calculus; chiral model; Ernst equation; Sylvester equation
 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.

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Language(s): eng - English
 Dates: 2011-12-23
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Method: Peer
 Identifiers: eDoc: 575682
DOI: 10.3842/SIGMA.2011.118
 Degree: -

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Title: Symmetry, Integrability and Geometry: Methods and Applications
  Alternative Title : SIGMA
Source Genre: Journal
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Affiliations:
Publ. Info: -
Pages: - Volume / Issue: 7 Sequence Number: 118 Start / End Page: - Identifier: -