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On Poisson geometries related to noncommutative emergent gravity

Autor(en)
Nikolaj Kuntner, Harold Steinacker
Abstrakt

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.

Organisation(en)
Mathematische Physik
Externe Organisation(en)
Universität Wien
Journal
Journal of Geometry and Physics
Band
62
Seiten
1760-1777
Anzahl der Seiten
18
ISSN
0393-0440
DOI
https://doi.org/10.1016/j.geomphys.2012.04.002
Publikationsdatum
2012
Peer-reviewed
Ja
ÖFOS 2012
103012 Hochenergiephysik, 103019 Mathematische Physik
Link zum Portal
https://ucrisportal.univie.ac.at/de/publications/c570be01-7ecd-49a7-b3e8-76e31f07e517