Gravitational non-commutativity and Gödel-like spacetimes

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dc.creatorDas, Saurya
dc.creatorGegenberg, Jack
dc.date2004-07-07
dc.date2008-02-01
dc.date.accessioned2026-07-07T11:59:17Z
dc.date.available2026-07-07T11:59:17Z
dc.descriptionWe 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 {\it 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.
dc.descriptionTwo sections added (Relation to the fuzzy sphere, Emergence of the star product). 10 pages, Revtex. To appear in General Relativity and Gravitation
dc.identifierhttps://arxiv.org/abs/hep-th/0407053
dc.identifierhttp://arxiv.org/abs/hep-th/0407053
dc.identifierGen.Rel.Grav.40:2115-2129,2008
dc.identifierdoi:10.1007/s10714-008-0619-3
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/206508
dc.subjectHigh Energy Physics - Theory
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleGravitational non-commutativity and Gödel-like spacetimes
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