U(2,2) gravity on noncommutative space with symplectic structure

The classical Einstein's gravity can be reformulated from the constrained U(2,2) gauge theory on the ordinary (commutative) four-dimensional spacetime. Here we consider a noncommutative manifold with a symplectic structure and construct a U(2,2) gauge theory on such a manifold by using the covariant coordinate method. Then we use the Seiberg-Witten map to express noncommutative quantities in terms of their commutative counterparts up to the first-order in noncommutative parameters. After imposing constraints we obtain a noncommutative gravity theory described by the Lagrangian with up to nonvanishing first order corrections in noncommutative parameters. This result coincides with our previous one obtained for the noncommutative SL(2,C) gravity.Comment: 13 pages, no figures; v2: 14 pages, clarifications and references added; v3: 16 pages, title changed, clarifications and references added; v4: 17 pages, clarifications added, this final version accepted by Physical Review

3-Bromo­anilinium picrate

In the title compound, C6H7BrN+·C6H2N3O7 −, the O atoms of two of the nitro groups are disordered over two sites, the ratios of the refined occupancies being 0.72 (6):0.28 (6) and 0.74 (5):0.26 (5). In the crystal structure, the anions and cations are linked via inter­molecular N—H⋯O hydrogen bonds into chains along [100]. Further stabilization is provided by weak inter­molecular C—H⋯O hydrogen bonds