# Behaviour of a spin-1/2 particle in Schwarzschild embedded in an electromagnetic universe

## TL;DR

This paper analyzes the behavior of a charged spin-1/2 particle in a Schwarzschild black hole environment immersed in an electromagnetic universe, deriving wave equations and studying potential effects of charge and frequency.

## Contribution

It derives Schrödinger-type wave equations for a charged spin-1/2 particle in this setting and examines how external electromagnetic parameters influence the potentials.

## Key findings

- Effective potentials depend on charge and frequency.
- Electromagnetic environment modifies particle behavior.
- Angular equations resemble Schwarzschild geometry.

## Abstract

The Dirac equation is considered in Schwarzschild black hole immersed in an electromagnetic universe with charge coupling. The equations of the charged spin-1/2 particle is separated into radial and angular equations by adopting the Newman-Penrose formalism. The angular equations obtained are similar to the Schwarzschild geometry. For the radial equations we manage to obtain the one dimensional Schr\"odinger-type wave equations with effective potentials. Due to the presence of electromagnetic field from the surroundings, the interaction with the charged spin-1/2 is considered. Finally, we study the behaviour of the potentials by plotting them as a function of radial distance and expose the effect of the external parameter, charge and the frequency of the particle on them.