On Poisson geometries related to noncommutative emergent gravity

JOURNAL OF GEOMETRY AND PHYSICS

卷:62

Article

Kuntner, Nikolaj¹  Steinacker, Harold¹ 

[1] Univ Vienna, Fac Phys, A-1090 Vienna, Austria

关键词: Metric-compatible Poisson structure;    Emergent gravity;    Noncommutative branes;    Self-duality;    Compactified extra dimensions;   

DOI  :  10.1016/j.geomphys.2012.04.002

来源: Elsevier

【 摘 要 】

We study metric-compatible Poisson structures in the semi-classical limit of noncommutative emergent gravity. Space-time is realized as quantized symplectic submanifold embedded in R-D, whose effective metric depends on the embedding as well as on the Poisson structure. We study solutions of the equations of motion for the Poisson structure, focusing on a natural class of solutions such that the effective metric coincides with the embedding metric. This leads to i-(anti-) self-dual complexified Poisson structures in four space-time dimensions with Lorentzian signature. Solutions on manifolds with conformally flat metric are obtained and tools are developed which allow to systematically re-derive previous results, e.g. for the Schwarzschild metric. It turns out that the effective gauge coupling is related to the symplectic volume density, and may vary significantly over space-time. To avoid this problem, we consider in a second part space-time manifolds with compactified extra dimensions and split noncommutativity, where solutions with constant gauge coupling are obtained for several physically relevant geometries. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free