# The Dirac equation in Schwarzschild mass coupled to a Stationary Electromagnetic Field

## TL;DR

This paper analyzes the Dirac equation in a complex spacetime combining Schwarzschild and stationary electromagnetic fields, deriving exact solutions and studying potential effects of parameters on particle behavior.

## Contribution

It provides exact analytical solutions for the angular part and explores the influence of parameters on radial potentials in a combined gravitational and electromagnetic background.

## Key findings

- Exact solutions for angular equations obtained.
- Radial potentials analyzed as functions of parameters.
- Effects of twisting parameter and frequencies on potentials studied.

## Abstract

We study the Dirac equation in a spacetime that represents the nonlinear superposition of the Schwarzchild solution to an external, stationary electromagnetic Berttoti-Robinson solution. We separate the Dirac equation into radial and angular equations using Newman--Penrose formalism. We obtain exact analytical solutions of the angular equations. We manage to obtain the radial wave equations with effective potentials. Finally, we study the potentials by plotting them as a function of radial distance and examine the effect of the twisting parameter and the frequencies on the potentials.