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

Abstract

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. Cl\'ement, 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.