Goedel-type Universes and the Landau Problem

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.

Latex, 21 pages, 1 figure. v2 missing references to previous work on the subject added

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Cited by in corpus (36)

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• Scalar field perturbations of the Schwarzschild black hole in the Gödel Universe
• A gravito-electromagnetic analogy based on tidal tensors
• Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry
• The generalized Klein-Gordon oscillator in the background of cosmic string space-time with a linear potential in the Kaluza-Klein theory
• Relativistic Motions of Spin-Zero Quantum Oscillator Field in a Global Monopole Space-Time with External Potential and AB-effect
• Gravito-electromagnetic analogies
• Quantization of heterotic strings in a Goedel/Anti de Sitter spacetime and chronology protection
• Linear confinement of a scalar particle in a Gödel-type spacetime
• Fermions in Gödel-type background space-times with torsion and the Landau quantization
• An Exact String Theory Model of Closed Time-Like Curves and Cosmological Singularities
• Holographic Fluids with Vorticity and Analogue Gravity
• Supertube domain-walls and elimination of closed time-like curves in string theory
• Relativistic spin-0 Duffin-Kemmer-Petiau equation in Bonnor-Melvin-Lambda solution
• The generalized Klein-Gordon oscillator with position-dependent mass in a particular Gödel-type space-time
• Weyl fermions in a family of Gödel-type geometries with a topological defect
• String spectrum of curved string backgrounds obtained by T-duality and shifts of polar angles
• The Dirac Equation in (1+2)-dimensional Gürses space-time backgrounds
• Interacting dark energy: generic cosmological evolution for two scalar fields
• PDM Klein-Gordon particles in Gödel-type Som-Raychaudhuri cosmic string spacetime background
• Relativistic and nonrelativistic Landau levels for the noncommutative quantum Hall effect with anomalous magnetic moment in a conical Gödel-type spacetime
• Classical Particle in Presence of Magnetic Field, Hyperbolic Lobachevsky and Spherical Riemann Models
• Dirac fermions in a spinning conical Gödel-type spacetime
• Ground state of a bosonic massive charged particle in the presence of external fields in a Gödel-type spacetime
• Quantum influence of topological defects on a relativistic scalar particle with Cornell-type potential in cosmic string space-time with a spacelike dislocation
• PDM Klein-Gordon particles in Som-Raychaudhuri cosmic string spacetime with space-like dislocation and a non-uniform magnetic field: spacetime associated degeneracies, vorticity-energy, and charge-energy correlations
• Klein-Gordon particles in Gödel-type Som-Raychaudhuri cosmic string spacetime and the phenomenon of spacetime associated degeneracies
• Over-Rotating Supertube Backgrounds
• The Godel-Schrodinger Spacetime and Stringy Chronology Protection
• Generalized Duffin-Kemmer-Petiau oscillator under Aharonov-Bohm flux in topological defects backgrounds
• Angular Momentum and Gravimagnetization of the $\mathcal{N}=2$ SYM vacuum
• Rotation effects on the graphene wormhole energy levels
• Weyl Fermions in a Linear Class of Gödel-Type Space-Time Backgrounds
• Investigation of spin-$0$ massive charged particle subject to a homogeneous magnetic field with potentials in a topologically trivial flat class of Gödel-type space-time
• Exotic Newton-Hooke group, noncommutative plane and superconformal symmetry
• Schrödinger particle in magnetic and electric fields in Lobachevsky and Riemann spaces