Improved generating technique for D=5 supergravities and squashed Kaluza-Klein black holes

Recently we suggested a solution-generating technique for five-dimensional supergravity with three Abelian vector fields based on the hidden SO(4,4) symmetry of the three-dimensionally reduced theory. This technique generalizes the G(2(2)) generating technique developed earlier for minimal five-dimensional supergravity (A. Bouchareb, G. Clement, C-M. Chen, D. V. Gal'tsov, N. G. Scherbluk, and Th. Wolf, Phys. Rev. D 76, 104032 (2007)) and provides a new matrix representation for cosets forming the corresponding sigma-models in both cases. Here we further improve these methods introducing a matrix-valued dualization procedure which helps to avoid difficulties associated with solving the dualization equations in the component form. This new approach is used to generate a five-parametric rotating charged Kaluza-Klein black hole with the squashed 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.