Gravitational non-commutativity and G\"odel-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 {\it 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.Comment: Two sections added (Relation to the fuzzy sphere, Emergence of the star product). 10 pages, Revtex. To appear in General Relativity and Gravitatio

G\"{o}del black hole, closed timelike horizon, and the study of particle emissions

We show that a particle, with positive orbital angular momentum, following an outgoing null/timelike geodesic, shall never reach the closed timelike horizon (CTH) present in the $(4+1)$-dimensional rotating G\"{o}del black hole space-time. Therefore a large part of this space-time remains inaccessible to a large class of geodesic observers, depending on the conserved quantities associated with them. We discuss how this fact and the existence of the closed timelike curves present in the asymptotic region make the quantum field theoretic study of the Hawking radiation, where the asymptotic observer states are a pre-requisite, unclear. However, the semiclassical approach provides an alternative to verify the Smarr formula derived recently for the rotating G\"{o}del black hole. We present a systematic analysis of particle emissions, specifically for scalars, charged Dirac spinors and vectors, from this black hole via the semiclassical complex path method.Comment: 13 pages; minor changes, references adde

Energy and Angular Momentum Densities in a Godel-Type Universe in the Teleparallel Geometry

The main scope of this research consists in evaluating the energy-momentum (gravitational field plus matter) and gravitational angular momentum densities in the universe with global rotation, considering the Godel-Obukhov metric. For this, we use the Hamiltonian formalism of the Teleparallel Equivalent of General Relativity (TEGR), which is justified for presenting covariant expressions for the considered quantities. We found that the total energy density calculated by the TEGR method is in agreement with the results reported by other authors in the literature using pseudotensors. The result found for the angular momentum density depends on the rotational parameter as expected. We also show explicitly the equivalence among the field equations of the TEGR and Einstein equations (RG), considering a perfect fluid and Godel-Obukhov metric.Comment: 20 pages, no figures. Revised in view of Referee's comments. Version to appear in the Gravitation and Cosmolog