Gravitational non-commutativity and Gödel-like spacetimes
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Date
2016-01-25
Authors
Das, Saurya
Gegenberg, Jack
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Abstract
We derive general conditions under which geodesics of stationary spacetimes resemble trajectories
of charged particles in an electromagnetic field. For large curvatures (analogous to strong magnetic
fields), the quantum mechanicical states of these particles are confined to gravitational analogs of
lowest Landau levels. Furthermore, there is an effective non-commutativity between their spatial
coordinates. We point out that the Som-Raychaudhuri and G¨odel spacetime and its generalisations
are precisely of the above type and compute the effective non-commutativities that they induce.
We show that the non-commutativity for G¨odel spacetime is identical to that on the fuzzy sphere.
Finally, we show how the star product naturally emerges in Som-Raychaudhuri spacetimes.
Description
Sherpa Romeo green journal. Permission to archive author manuscript.
Keywords
Non-commutative geometry , Matrix models , Non-perturbative effects , Gödel spacetime
Citation
Das, S., & Gegenberg, J. (2008). Gravitational con-commutativity and Gödel-like spacetimes. General Relativity and Gravitation, 40(10), 2115-2129. doi: 10.1007/s10714-008-0619-3