Abstract
In this contribution, some solutions of the Klein–Gordon equation in Godel-type metrics with an embedded cosmic string are considered. The quantum dynamics of a scalar particle in three spaces whose metrics are described by different classes of Godel solutions, 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.
Highlights
Drukker et al [15] have investigated a close relation between a class of Gödel solutions for general relativity in (3 + 1)-dimensions and the Landau problem in a space of constant curvature
In Ref. [16] the same relation between the flat Gödel solution (Som and Raychaudhuri limit) and Landau problem in the flat space was obtained. In another way the Landau problem was investigated in several situations, for example, in a hyperbolic space [17,18], in a spherical space [18], in the presence of topological defects [19,20,21], for neutral particles [22,23,24,25] and for non-inertial frames in a cosmic string background [26]
We studied the impact of the presence of topological defects in the family of Gödel-type space-times on the energy levels of a scalar quantum particle in this geometry
Summary
Drukker et al [15] have investigated a close relation between a class of Gödel solutions for general relativity in (3 + 1)-dimensions and the Landau problem in a space of constant curvature. [16] the same relation between the flat Gödel solution (Som and Raychaudhuri limit) and Landau problem in the flat space was obtained In another way the Landau problem was investigated in several situations, for example, in a hyperbolic space [17,18], in a spherical space [18], in the presence of topological defects [19,20,21], for neutral particles [22,23,24,25] and for non-inertial frames in a cosmic string background [26]. In the concluding remarks, we present a discussion of the main results we obtained
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