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This article is cited in 11 scientific papers (total in 11 papers)
Binary Darboux Transformations in Bidifferential Calculus and Integrable Reductions of Vacuum Einstein Equations
Aristophanes Dimakisa, Folkert Müller-Hoissenb a Department of Financial and Management Engineering, University of the Aegean, 82100 Chios, Greece
b Max-Planck-Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
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).
Keywords:
bidifferential calculus; binary Darboux transformation; chiral model; Einstein equations; black ring.
Received: November 12, 2012; in final form January 29, 2013; Published online February 2, 2013
Citation:
Aristophanes Dimakis, Folkert Müller-Hoissen, “Binary Darboux Transformations in Bidifferential Calculus and Integrable Reductions of Vacuum Einstein Equations”, SIGMA, 9 (2013), 009, 31 pp.
Linking options:
https://www.mathnet.ru/eng/sigma792 https://www.mathnet.ru/eng/sigma/v9/p9
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