Goedel-type Universes and the Landau Problem

We point out a close relation between a family of Goedel-type solutions of 3+1 General Relativity and the Landau problem in S^2, R^2 and H_2; in particular, the classical geodesics correspond to Larmor orbits in the Landau problem. We discuss the extent of this relation, by analyzing the solutions of the Klein-Gordon equation in these backgrounds. For the R^2 case, this relation was independently noticed in hep-th/0306148. Guided by the analogy with the Landau problem, we speculate on the possible holographic description of a single chronologically safe region.Comment: Latex, 21 pages, 1 figure. v2 missing references to previous work on the subject adde

Closed Timelike Curves and Holography in Compact Plane Waves

We discuss plane wave backgrounds of string theory and their relation to Goedel-like universes. This involves a twisted compactification along the direction of propagation of the wave, which induces closed timelike curves. We show, however, that no such curves are geodesic. The particle geodesics and the preferred holographic screens we find are qualitatively different from those in the Goedel-like universes. Of the two types of preferred screen, only one is suited to dimensional reduction and/or T-duality, and this provides a ``holographic protection'' of chronology. The other type of screen, relevant to an observer localized in all directions, is constructed both for the compact and non-compact plane waves, a result of possible independent interest. We comment on the consistency of field theory in such spaces, in which there are closed timelike (and null) curves but no closed timelike (or null) geodesics.Comment: 21 pages, 3 figures, LaTe