Quantum influence of topological defects in Gödel-type space-times

Abstract

In this contribution, some solutions of the Klein-Gordon equation in the Gödel-type metrics with an embedded cosmic string are considered. The quantum dynamics of a scalar particle in three spaces whose metric is described by different classes of Gödel solution, with a cosmic string passing through the spaces, is found. The energy levels and eigenfunctions of the Klein-Gordon operator are obtained. We show that these eigenvalues and eigenfunctions depend on the parameter characterizing the presence of a cosmic string in the space-time. We note that the presence of topological defects breaks the degeneracy of energy levels.

Klein–Gordon oscillator in Kaluza–Klein theory

“…In the limit of = 0, a spectrum similar to the Landau levels is recovered. 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.…”

“…This is equivalent to the energy levels in the Gödel-type spacetimes studied by us [59][60][61]64]. Although Eq.…”

“…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.…”

Investigation of DKP equation for spin-zero system in the presence of Gödel-type background space-time

“…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]. The solutions of the Klein-Gordon equation in the background of KerrNewman, Gödel and Friedmann-Robertson-Walker spacetimes with a cosmic string passing through them have been obtained; some of their consequences have been discussed, with emphasis on the role played by the presence of the cosmic string [10].…”

“…In this case, we have the new coordinates R = i 2l and θ = r R [9]; then the line element (2.1) becomes…”