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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, the

The local and the global structures of space-time play an important role in the behavior of quantum systems. In this aspect, it is believed that global features of space-time may be directly related to the shift of energy levels of quantum particles. In the particular case of the

On the other hand, in quantum mechanics the harmonic oscillator is one of the most significant systems to be studied. In recent years, the relativistic version of the harmonic oscillator has been considered in several studies [

Another aspect of interest in our work is the influence of noninertial effects on quantum systems. As in classical physics, quantum mechanics is sensitive to the use of noninertial reference systems. These effects can be taken into account through an appropriate coordinate transformation. Previous research reported in literature [

Therefore, in this contribution, we will study bosons in the

This work is organized as follows: In Section

In this section, we define the line element that describes the space-time geometry in agreement with the proposal of this work. We want to study the behavior of massive scalar fields (zero spin particles) under the influence of a gravitational field generated by a space-time with the nontrivial topology

Representation of the topologically nontrivial space-time

The metric in polar coordinates describing the space-time under consideration is described by the expression

We can see that both

In this section we study the KG oscillator in a geometry

Let us now study the KG oscillator. Such a procedure is similar to one that is carried out for the insertion of an electromagnetic interaction which is made by the introduction of a 4-vector potential external

The wave function

The plots of

It is interesting to note that the energy is symmetric around

The plots of

In this section, we will study the influence of noninertial effects of a referential in rotation in a space-time with nontrivial topology, applied to the KG wave equation with a KG oscillator potential. Therefore, based on the procedures that were discussed in the previous section, in our computational developments that will be developed here, we will first recast the differential equation for the KG oscillator in the space-time described by the line element of (

Now the energy spectrum depends on the angular velocity of the frame. The first term is related to the noninertial effects and appears frequently in this type of physical system. The second term is the usual energy spectrum of an inertial frame. As it can be seen in Figure

The plots of

In this work, we have determined solutions of the KG oscillator in a topologically nontrivial space-time. We have considered two different settings in this space. In the first case the usual

Additionally, we have shown that the space-time topology modifies the energy spectrum. In fact, the

No data were used to support this study.

The authors declare that they have no conflicts of interest.

This work was supported in part by means of funds provided by CAPES.

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