https://doi.org/10.1140/epjc/s10052-008-0602-x
Regular Article - Theoretical Physics
The energy-momentum of a Poisson structure
1
Faculty of Physics, University of Belgrade, P.O. Box 368, 11001, Belgrade, Serbia
2
Laboratoire de Physique Théorique, Université de Paris-Sud, Bâtiment 211, 91405, Orsay, France
3
Physics Department, National Technical University, Zografou Campus, 15780, Zografou, Athens, Greece
* e-mail: majab@phy.bg.ac.yu
Received:
27
February
2008
Published online:
6
May
2008
Consider the quasi-commutative approximation to a noncommutative geometry. It is shown that there is a natural map from the resulting Poisson structure to the Riemann curvature of a metric. This map is applied to the study of high-frequency gravitational radiation. In classical gravity in the WKB approximation there are two results of interest, a dispersion relation and a conservation law. Both of these results can be extended to the noncommutative case, with the difference that they result from a cocycle condition on the high-frequency contribution to the Poisson structure, not from the field equations.
© Springer-Verlag , 2008
