Aristophanes Dimakis, Folkert Mueller-Hoissen
We present a general result within the bidifferential calculus approach to integrable partial differential and difference equations, which can be regarded as a quite universal formulation of a vectorial binary Darboux 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 saturn, bicycling black rings).
View original:
http://arxiv.org/abs/1207.1308
No comments:
Post a Comment