## G_2 generating technique for minimal D=5 supergravity and black rings

Please always quote using this URN: urn:nbn:de:0297-zib-11732
• 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.

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Author: Adel Bouchareb, Gérard Clément, Chiang-Mei Chen, Thomas Wolf, Dmitri V. Gal'tsov, Nikolai G. Scherbluk ZIB-Report Killing vectors; black rings; duality; supergravity 00.00.00 GENERAL / 04.00.00 General relativity and gravitation (for astrophysical aspects, see 95.30.Sf Relativity and gravitation; for relativistic aspects of cosmology, see 98.80.Jk); Special relativity, see 03.30.+p / 04.20.-q Classical general relativity (see also 02.40.-k Geometry, differential geometry, and topology) / 04.20.Jb Exact solutions Lab. de Physique Th. LAPTH (CNRS); Nat. Centr. Univ., Taiwan; Brock Univ., St. Catherines, Ontario; Moscow State Univ. 2010/07/05 ZIB-Report (10-14) http://arxiv.org/abs/0708.2361 1438-0064 Appeared in: Phys. Rev. D 76, 104032 (2007).