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 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.Comment: 20 pages, revtex

Three-charge 2J black ring

Using recently proposed new solution generating technique, we construct the charged version of Pomeranski-Senkov doubly rotating black ring in the $U(1)^3$ five-dimensional supergravity. For arbitrary values of charges the solution is unbalanced, but the Dirac-Misner string is removed when two of the charges are set to zero. In this particular case our solution can be uplifted to some solution of six-dimensional vacuum gravity.Comment: 9 pages revtex

G2G_2 generating technique for minimal D=5 supergravity and black rings

A solution generating technique is developed for D=5 minimal supergravity with two commuting Killing vectors based on the $G_2$ U-duality arising in the reduction of the theory to three dimensions. The target space of the corresponding 3-dimensional sigma-model is the coset $G_{2(2)}/(SL(2,R)\times SL(2,R))$. Its isometries constitute the set of solution generating symmetries. These include two electric and two magnetic Harrison transformations with the corresponding two pairs of gauge transformations, three $SL(2,R) S$-duality transformations, and the three gravitational scale, gauge and Ehlers transformations (altogether 14). We construct a representation of the coset in terms of $7\times 7$ matrices realizing the automorphisms of split octonions. Generating a new solution amounts to transforming the coset matrices by one-parametric subgroups of $G_{2(2)}$ and subsequently solving the dualization equations. Using this formalism we derive a new charged black ring solution with two independent parameters of rotation.Comment: 21 pages revtex-4, 1 figure, typo corrected in Eq. (103

Generating technique for U(1)35DU(1)^3 5D supergravity

We develop generating technique for solutions of $U(1)^3 5D$ supergravity via dimensional reduction to three dimensions. This theory, which recently attracted attention in connection with black rings, can be viewed as consistent truncation of the $T^6$ compactification of the eleven-dimensional supergravity. Its further reduction to three dimensions accompanied by dualisation of the vector fields leads to 3D gravity coupled sigma model on the homogeneous space $SO(4,4)/SO(4)\times SO(4)$ or $SO(4,4)/SO(2,2)\times SO(2,2)$ depending on the signature of the three-space. We construct a $8\times 8$ matrix representation of these cosets in terms of lower-dimensional blocks. Using it we express solution generating transformations in terms of the potentials and identify those preserving asymptotic conditions relevant to black holes and black rings. As an application, we derive the doubly rotating black hole solution with three independent charges. A suitable contraction of the above cosets is used to construct a new representation of the coset $G_{2(2)}/(SL(2,R)\times SL(2,R))$ relevant for minimal five-dimensional supergravity.Comment: A typo in Sec. VII B corrected, some references adde