# A central potential with a massive scalar field in a Lorentz symmetry violation environment

## TL;DR

This paper explores how a massive scalar field behaves under Coulomb and linear potentials within a Lorentz-violating environment, providing analytical solutions to the modified Klein-Gordon equation.

## Contribution

It introduces a novel analysis of scalar fields in Lorentz-violating spacetime with specific potentials, deriving analytical solutions to the modified Klein-Gordon equation.

## Key findings

- Analytical solutions obtained for the Klein-Gordon equation with Lorentz violation.
- Demonstrates the impact of Lorentz symmetry breaking on scalar field behavior.
- Provides insights into potential modifications of quantum field dynamics in Lorentz-violating backgrounds.

## Abstract

We investigate the behaviour of a massive scalar field under the influence of a Coulomb-type and central linear central potentials inserted in the Klein-Gordon equation by modifying the mass term in the spacetime with Lorentz symmetry violation. We consider the presence of a background constant vector field which characterizes the breaking of the Lorentz symmetry and show that analytical solutions to the Klein-Gordon equation can be achieved.