Goedel-type Universes and the Landau Problem

TL;DR

This paper explores the connection between Goedel-type solutions in general relativity and the Landau problem, analyzing classical and quantum behaviors, and speculating on holographic interpretations of these spacetimes.

Contribution

It establishes a novel analogy between Goedel-type universes and the Landau problem, including classical geodesics and Klein-Gordon solutions, and discusses potential holographic implications.

Findings

Classical geodesics match Larmor orbits in the Landau problem.

The Klein-Gordon equation solutions reflect the Landau problem structure.

The R^2 case relation was independently identified in prior work.

Abstract

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.