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

Symmetry Integrability and Geometry-Methods and Applications

article

Aristophanes Dimakis¹  Folkert Müller-Hoissen² 

[1] Department of Financial and Management Engineering, University of the Aegean;Max-Planck-Institute for Dynamics and Self-Organization

关键词: bidif ferential calculus;    binary Darboux transformation;    chiral model;    Einstein equations;    black ring;   

DOI  :  10.3842/SIGMA.2013.009

来源: National Academy of Science of Ukraine

【 摘 要 】

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).

【 授权许可】

Unknown