Einstein Equations for a Noncommutative Spacetime of Lie-Algebraic Type

作者: Marcos Rosenbaum , José David Vergara , Albert Much , Diego Vidal-Cruzprieto

DOI:

关键词:

摘要: A general formula is calculated for the connection of a central metric w.r.t.\ noncommutative spacetime Lie-algebraic type. This done by using framework linear connections on bi-modules. The further used to calculate corresponding Riemann tensor and prove Bianchi identities certain symmetries that are essential obtain symmetric divergenceless Einstein Tensor. In particular, obtained Tensor not equivalent sum scalar, as in commutative case, but addition traceless term appears.

参考文章(14)
Marcos Rosenbaum, Small-Scale Structure of Space-Time and Dirac Operator International Journal of Theoretical Physics. ,vol. 40, pp. 139- 163 ,(2001) , 10.1023/A:1003783327275
P. P. Kulish, M. Dimitrijević, J. Wess, F. Lizzi, P. Aschieri, Noncommutative Spacetimes: Symmetries in Noncommutative Geometry and Field Theory ,(2009)
Sergey Solodukhin, Peter Schupp, Exact Black Hole Solutions in Noncommutative Gravity arXiv: High Energy Physics - Theory. ,(2009)
Paolo Aschieri, Leonardo Castellani, Noncommutative gravity solutions Journal of Geometry and Physics. ,vol. 60, pp. 375- 393 ,(2010) , 10.1016/J.GEOMPHYS.2009.11.009
Ali H. Chamseddine, Alain Connes, Universal Formula for Noncommutative Geometry Actions: Unification of Gravity and the Standard Model Physical Review Letters. ,vol. 77, pp. 4868- 4871 ,(1996) , 10.1103/PHYSREVLETT.77.4868
Paolo Aschieri, Christian Blohmann, Marija Dimitrijević, Frank Meyer, Peter Schupp, Julius Wess, A gravity theory on noncommutative spaces Classical and Quantum Gravity. ,vol. 22, pp. 3511- 3532 ,(2005) , 10.1088/0264-9381/22/17/011
Paula Tretkoff, Alain Connes, The Gauss-Bonnet Theorem for the noncommutative two torus arXiv: Quantum Algebra. ,(2009)