SL(2,C) gravity on noncommutative space with Poisson structure

The Einstein's gravity theory can be formulated as an SL(2,C) gauge theory in terms of spinor notations. In this paper, we consider a noncommutative space with the Poisson structure and construct an SL(2,C) formulation of gravity on such a space. Using the covariant coordinate technique, we build a gauge invariant action in which, according to the Seiberg-Witten map, the physical degrees of freedom are expressed in terms of their commutative counterparts up to the first order in noncommutative parameters.Comment: 12 pages, no figures; v2: 13 pages, clarifications and references added; v3: clarifications added; v4: more clarifications and references added, final version to appear in Phys. Rev.

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

Noncommutative corrections to the minimal surface areas of the pure AdS spacetime and Schwarzschild-AdS black hole

Based on the perturbation expansion method, we compute the noncommutative corrections to the minimal surface areas of the pure AdS spacetime and Schwarzschild-AdS black hole, where the noncommutaitve background is suitably constructed in terms of the Poincar\'e coordinate system. In particular, we find a reasonable tetrad with subtlety, which not only matches the metrics of the pure AdS spacetime and Schwarzschild-AdS black hole in the commutative case, but also makes the corrections real rather than complex in the noncommutative case. For the pure AdS spacetime, the nocommutaitve effect is only a logarithmic term, while for the Schwarzchild-AdS black hole, it contains a logarithmic contribution plus a both mass and noncommutative parameter related term.Comment: v1: 10 pages, no figures; v2: 11 pages, minor clarifications and references added; v3: minor revisons and references added

Diaqua­bis­(4-carb­oxy-2-ethyl-1H-imidazole-5-carboxyl­ato-κ2 N 3,O 4)manganese(II) N,N-dimethyl­formamide disolvate

In the title compound, [Mn(C7H7N2O4)2(H2O)2]·2C3H7NO, the central MnII ion, located on an inversion center, is hexa­coordinated by four O atoms from two water mol­ecules and two carboxyl­ate groups, and two N atoms from two 4-carb­oxy-2-ethyl-1H-imidazole-5-carboxyl­ate anions in a slightly distorted octa­hedral environment. The complex mol­ecules and solvent mol­ecules are connected via N—H⋯O and O—H⋯O hydrogen bonds into a two-dimensional polymeric structure parallel to (001)