Gödel-type universes and the Landau problem

Drukker, Nadav; Fiol, Bartomeu; Simón, Joan

doi:10.1088/1475-7516/2004/10/012

Cited by 71 publications

(106 citation statements)

References 49 publications

(121 reference statements)

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“…Note that this dynamics in the presence of the confining potential due to the Klein-Gordon oscillator reinforces the characteristics of the quantum dynamics observed in this Gödel-type spacetime [59][60][61], which are characterized by the similarity with the Landau problem for a charged particle on a surface exposed to a uniform magnetic field. Based on this analogy, Druker et al [59] have suggested the picture of a holographic description for a single chronologically safe region. In the same paper they have conjectured that this discussion can be extended for a 4 + 1-dimensonal Gödel solution.…”

Section: Discussionsupporting

confidence: 76%

“…One of these theories was developed by Gödel in the 1950s for an universe with rigid rotation characterized by a term in the metric and with a curvature source known as a Weyssenhoff-Raabe fluid [56,57]. Some studies of the quantum dynamics in this spacetime were carried out for (3 + 1)-dimensional spacetimes [58][59][60]. In this section we consider a cosmic dispiration in a flat Gödel solution or SomRaychaudhuri solution in Kaluza-Klein theory.…”

Section: Kg Oscillator In Cosmic Dislocation In Som-raychaudhuri Spacmentioning

confidence: 99%

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Klein–Gordon oscillator in Kaluza–Klein theory

et al. 2016

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In this contribution we study the Klein-Gordon oscillator on the curved background within the Kaluza-Klein theory. The problem of the interaction between particles coupled harmonically with topological defects in Kaluza-Klein theory is studied. We consider a series of topological defects, then we treat the Klein-Gordon oscillator coupled to this background, and we find the energy levels and corresponding eigenfunctions in these cases. We show that the energy levels depend on the global parameters characterizing these spacetimes. We also investigate a quantum particle described by the Klein-Gordon oscillator interacting with a cosmic dislocation in Som-Raychaudhuri spacetime in the presence of homogeneous magnetic field in a Kaluza-Klein theory. In this case, the energy spectrum is determined, and we observe that these energy levels represent themselves as the sum of the terms related with Aharonov-Bohm flux and of the parameter associated to the rotation of the spacetime.

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Section: Discussionsupporting

confidence: 76%

Section: Kg Oscillator In Cosmic Dislocation In Som-raychaudhuri Spacmentioning

confidence: 99%

Klein–Gordon oscillator in Kaluza–Klein theory

et al. 2016

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“…This expression is analogous to the vector potential that yields a uniform magnetic field in the z-direction. An interesting property of this type of metric is that the geodesics for this spacetime are circles, which have a physical description similar to Larmor orbits for an electron that moves in a perpendicular magnetic field [8,9]. This analogy also arises from the point of view of quantum mechanics, where the quantum dynamics of scalar and spinorial quantum particles in this spacetime is an analogue of the Landau levels, as observed in Refs.…”

Section: Linear Confinement In the Som-raychaudhuri Spacetime With A mentioning

confidence: 80%

“…[7], the first study of this problem was made, where the KleinGordon and Dirac equations in the Gödel-type spacetimes with positive and negative curvatures were investigated, and also in a flat Gödel-type spacetime. Further, the investigation of the relationship between the quantum dynamics of the scalar quantum particle in background of general relativity with Gödel solutions and the Landau levels in the flat, spherical and hyperbolic spaces was performed by Drukker et al [8]. They analyzed the similarity between the spectrum of the energy of a scalar quantum particle in these class of Gödel-type spacetimes and the Landau levels in curved backgrounds.…”

Section: Introductionmentioning

confidence: 99%

Linear confinement of a scalar particle in a Gödel-type spacetime

2018

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Based on the studies of confinement of quarks, we introduce a linear scalar potential into the relativistic quantum dynamics of a scalar particle. Then we analyze the linear confinement of a relativistic scalar particle in a Gödel-type spacetime in the presence of a topological defect. We consider a Gödel-type spacetime associated with null curvature, i.e., the Som-Raychaudhuri spacetime, which is characterized by the presence of vorticity in the spacetime. Then we search for analytical solutions to the Klein-Gordon equation and analyze the influence of the topology of the cosmic string and the vorticity on the relativistic energy levels.

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“…As an application of Gödel-type problems in the relativistic studied we can indicate that gravitational coupling of Klein-Gordon and Dirac fields to matter vorticity and spacetime torsion, in the context of Einstein-Cartan theory with a e-mail: hha1349@gmail.com b e-mail: mimip44@naver.net c e-mail: soroushzrg@gmail.com d e-mail: hadisobhani8637@gmail.com a Gödel-type metric, have been done by Figueiredo [7]. A close relation was seen between a family of Gödel-type solutions of 3+1 general relativity and the Landau problem, as reported by Drukker [8]. The quantum dynamics of a scalar particle in three spaces whose metrics are described by different classes of Gödel solutions, with a cosmic string passing through the spaces has been studied [9].…”

Section: Introductionmentioning

confidence: 93%