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Recently we suggested a solution generating technique for five-dimensionalsupergravity with three Abelian vector fields based on the hidden SO(4,4)symmetry of the three-dimensionally reduced theory. This technique generalizesthe $G_{2(2)}$ generating technique developed earlier for minimal 5Dsupergravity (A. Bouchareb, G. Cl\'ement, C-M. Chen, D. V. Gal'tsov, N. G.Scherbluk, and Th. Wolf, Phys. Rev. D {\bf 76}, 104032 (2007)) and provides anew matrix representation for cosets forming the corresponding sigma-models inboth cases. Here we further improve these methods introducing a matrix-valueddualisation procedure which helps to avoid difficulties associated with solvingthe dualisation equations in the component form. This new approach is used togenerate a five-parametric rotating charged Kaluza-Klein black hole with thesquashed horizon adding one parameter more to the recent solution by Tomizawa,Yasui and Morisawa which was constructed using the previous version of the$G_{2(2)}$ generating technique.

Improved generating technique for D=5 supergravities and squashed Kaluza-Klein Black Holes