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  Binary Darboux transformations in bidifferential calculus and integrable reductions of vacuum Einstein equations

Dimakis, A., & Müller-Hoissen, F. (2013). Binary Darboux transformations in bidifferential calculus and integrable reductions of vacuum Einstein equations. Symmetry, Integrability and Geometry: Methods and Applications, 9: 009. doi:10.3842/SIGMA.2013.009.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-102D-9 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-102E-7
Genre: Journal Article

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 Creators:
Dimakis, Aristophanes, 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; binary Darboux transformation; chiral model; Einstein equations; black ring
 Abstract: We present a general solution-generating result within the bidifferential calculus approach to integrable partial differential and difference equations, based on a binary Darboux-type transformation. This is then applied to the non-autonomous chiral model, a certain reduction of which is known to appear in the case of the D-dimensional vacuum Einstein equations with D−2 commuting Killing vector fields. A large class of exact solutions is obtained, and the aforementioned reduction is implemented. This results in an alternative to the well-known Belinski-Zakharov formalism. We recover relevant examples of space-times in dimensions four (Kerr-NUT, Tomimatsu-Sato) and five (single and double Myers-Perry black holes, black saturn, bicycling black rings).

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Language(s): eng - English
 Dates: 2013-02-03
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Method: Peer
 Degree: -

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Title: Symmetry, Integrability and Geometry: Methods and Applications
  Alternative Title : SIGMA
Source Genre: Journal
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Publ. Info: -
Pages: - Volume / Issue: 9 Sequence Number: 009 Start / End Page: - Identifier: -