# Heun-type solutions for Schwarzschild metric with electromagnetic fields

## TL;DR

This paper derives confluent Heun function solutions for radial equations of specific black hole metrics with electromagnetic fields, advancing analytical methods in curved spacetime physics.

## Contribution

It introduces explicit confluent Heun solutions for the radial equations of two Halilsoy-Badawi metrics involving electromagnetic fields.

## Key findings

- Derived Heun solutions for the Dirac equation in the first metric.
- Obtained Heun solutions for the Klein-Gordon equation in the second metric.
- Enhanced analytical understanding of wave equations in these black hole backgrounds.

## Abstract

We find confluent Heun solutions to the radial equations of two Halilsoy-Badawi metrics. For the first metric, we studied the radial part of the massless Dirac equation and for the second case, we studied the radial part of the massless Klein-Gordon equation.