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arXiv · 1207.1308

Binary Darboux Transformations in Bidifferential Calculus and Integrable Reductions of Vacuum Einstein Equations

Aristophanes Dimakis·Folkert Müller-Hoissen
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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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BibTeXRIS

Aristophanes Dimakis, Folkert Müller-Hoissen. 2013-02-02. Binary Darboux Transformations in Bidifferential Calculus and Integrable Reductions of Vacuum Einstein Equations. https://doi.org/10.3842/sigma.2013.009

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