# Klein-Gordon oscillator in a topologically nontrivial space-time

## TL;DR

This paper investigates the Klein-Gordon oscillator in a topologically nontrivial space-time, deriving energy spectra and wave functions for different configurations, revealing symmetry-breaking effects in rotating frames.

## Contribution

It provides new analytical solutions for the Klein-Gordon oscillator in nontrivial topologies, including rotating frames, with explicit energy spectra and wave functions.

## Key findings

- Derived compact energy spectra for both configurations.
- Found that rotation introduces symmetry-breaking in the energy spectrum.
- Provided explicit wave functions for scalar particles in these topologies.

## Abstract

In this study, we analyze solutions of the wave equation for scalar particles in a space-time with nontrivial topology. Solutions for the Klein--Gordon oscillator are found considering two configurations of this space-time. In the first one, it is assumed the $S^{1}\times R^{3}$ space where the metric is written in the usual inertial frame of reference. In the second case, we consider a rotating reference frame adapted to the circle S1. We obtained compact expressions for the energy spectrum and for the particles wave functions in both configurations. Additionally, we show that the energy spectrum of the solution associated to the rotating system has an additional term that breaks the symmetry around $E = 0$.