The Energy-momentum of a Poisson structure

Details The Energy-momentum of a Poisson structure The Energy-momentum of a Poisson structure

2007-09-20

arxiv.org/abs/0709.3159v1

Eur.Phys.J.C55:489-498,2008

Physics

High Energy Physics

High Energy Physics - Theory

22 pages

Scientific paper

10.1140/epjc/s10052-008-0602-x

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.

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