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

TL;DR

This paper introduces an improved solution generating technique for five-dimensional supergravity, enabling the construction of more general black hole solutions with squashed horizons by utilizing a matrix-valued dualisation approach.

Contribution

It develops a new matrix-valued dualisation method that enhances existing solution generating techniques for 5D supergravity, allowing for more complex black hole solutions.

Findings

Generated a five-parametric rotating charged Kaluza-Klein black hole with squashed horizon.

Added one parameter to the previous solution by Tomizawa, Yasui, and Morisawa.

Improved the matrix representation for cosets in supergravity sigma-models.

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 5D supergravity (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 a new matrix representation for cosets forming the corresponding sigma-models in both cases. Here we further improve these methods introducing a matrix-valued dualisation procedure which helps to avoid difficulties associated with solving the dualisation 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.