# Heun-type solutions of the Klein--Gordon and Dirac equations in the Garfinkle--Horowitz--Strominger dilaton black hole background

## TL;DR

This paper derives solutions to the Klein-Gordon and Dirac equations in a Garfinkle-Horowitz-Strominger black hole background using Heun confluent functions, providing an alternative to the Newman-Penrose formalism.

## Contribution

It introduces a gauge covariant approach to solve these equations, expressing solutions in terms of Heun functions, which is a novel method in this context.

## Key findings

- Solutions expressed in terms of Heun confluent functions.
- Alternative approach to Newman-Penrose formalism.
- Discussion of properties of the solutions.

## Abstract

We study the Klein-Gordon and the Dirac equations in the background of the Garfinkle-Horowitz-Strominger black hole, in the Einstein frame. Using a $SO(3,1) \times U(1)-$gauge covariant approach, as an alternative to the Newman-Penrose formalism for the Dirac equation, it turns out that these solutions can be expressed in terms of Heun confluent functions and we discuss some of their properties.