Relativistic Landau levels in the rotating cosmic string spacetime

M S Cunha,V B Bezerra,H R Christiansen,C R Muniz

doi:10.1140/epjc/s10052-016-4357-5

Abstract

In the spacetime induced by a rotating cosmic string we compute the energy levels of a massive spinless particle coupled covariantly to a homogeneous magnetic field parallel to the string. Afterwards, we consider the addition of a scalar potential with a Coulomb-type and a linear confining term and completely solve the Klein-Gordon equations for each configuration. Finally, assuming rigid-wall boundary conditions, we find the Landau levels when the linear defect is itself magnetized. Remarkably, our analysis reveals that the Landau quantization occurs even in the absence of gauge fields provided the string is endowed with spin.

Highlights

A renewed interest in cosmic strings has been witnessed after a period of ostracism [1,2,3,4,5,6,7]
Cosmic strings are hypothetical massive objects that may have contributed, albeit marginally, to the anisotropy of the cosmic microwave background radiation and, to the large scale structure of the universe [8]. Their existence is supported in superstring theories with either compactified or extended extra dimensions. Both static and rotating cosmic strings can be responsible for some remarkable effects such as particle self-force [9,10] and gravitational lensing [11], as well as for production of highly energetic particles [12,13,14]
Cosmic string may eventually present an internal structure [20] generating a Gödel spacetime featuring an exotic region which allows closed time-like curves (CTC’s) around the singularity

Summary

Introduction

A renewed interest in cosmic strings has been witnessed after a period of ostracism [1,2,3,4,5,6,7]. To make some progress in this direction, we will present a fully relativistic study of a massive charged particle coupled to a gauge field in the spacetime spanned by a rotating string, with the eventual addition of scalar potentials. 2, we obtain the exact energy eigenvalues of the Klein–Gordon equation in the metric of a stationary rotating cosmic string coupled to a static magnetic field.

Results

Conclusion