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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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 Urheber:
Dimakis, Aristophanes, Autor
Müller-Hoissen, Folkert1, Autor           
Affiliations:
1Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063285              

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Schlagwörter: bidifferential calculus; binary Darboux transformation; chiral model; Einstein equations; black ring
 Zusammenfassung: 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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Sprache(n): eng - English
 Datum: 2013-02-03
 Publikationsstatus: Erschienen
 Seiten: -
 Ort, Verlag, Ausgabe: -
 Inhaltsverzeichnis: -
 Art der Begutachtung: Expertenbegutachtung
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Titel: Symmetry, Integrability and Geometry: Methods and Applications
  Alternativer Titel : SIGMA
Genre der Quelle: Zeitschrift
 Urheber:
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Ort, Verlag, Ausgabe: -
Seiten: - Band / Heft: 9 Artikelnummer: 009 Start- / Endseite: - Identifikator: -