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- Title
Gravitational non-commutativity and Gödel-like spacetimes.
- Authors
Saurya Das; Jack Gegenberg
- Abstract
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 Gödel 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 Gödel spacetime is identical to that on the fuzzy sphere. Finally, we show how the star product naturally emerges in Som–Raychaudhuri spacetimes.
- Subjects
MAGNETIC fields; FIELD theory (Physics); GEOMAGNETISM; MAGNETICS
- Publication
General Relativity & Gravitation, 2008, Vol 40, Issue 10, p2115
- ISSN
0001-7701
- Publication type
Article
- DOI
10.1007/s10714-008-0619-3