Complete integrability of higher-dimensional Einstein equations with additional symmetry and rotating black holes

A new derivation of the five-dimensional Myers-Perry black-hole metric as a 2-soliton solution on a nonflat background is presented. It is intended to be an illustration of how the well-known Belinski-Zakharov method can be applied to find solutions of the Einstein equations in $D$-dimensional space-time with $D-2$ commuting Killing vectors using the complete integrability of this system. The method appears also to be promising for the analysis of the uniqueness questions for higher-dimensional black holes.