Gravitational non-commutativity and Gödel-like spacetimes
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.
Sherpa Romeo green journal. Permission to archive author manuscript.
Non-commutative geometry , Matrix models , Non-perturbative effects , Gödel spacetime
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