# Landau Levels in the Presence of a Cosmic String in Rainbow Gravity

## TL;DR

This paper investigates how rainbow gravity modifies Landau energy levels of a charged scalar particle in a cosmic string spacetime, providing exact formulas for different models in both non-relativistic and relativistic regimes.

## Contribution

It derives exact Landau level expressions in rainbow gravity models for the first time in cosmic string spacetime, comparing them with standard gravity results.

## Key findings

- Rainbow gravity alters Landau levels significantly.
- Different rainbow models produce distinct energy shifts.
- Results applicable to quantum systems in curved spacetime environments.

## Abstract

In this paper we analyze the energy levels of a charged scalar particle placed in the static cosmic string spacetime, under the action of a uniform magnetic field parallel to the string, in the context of the semi-classical approach of the rainbow gravity. Firstly, we focus on the non-relativistic regime by solving the corresponding Schr\"{o}dinger equation, following by a complete relativistic treatment of the problem in which we considered the Klein-Gordon equation. In both cases we find exact expressions for the Landau levels in terms of the rainbow functions, used to characterize a rainbow gravity model. In order to achieve the results of this paper we considered three different rainbow gravity models mostly used in the literature and compare the resulting modifications in the Landau levels with the standard case, namely without rainbow gravity.