# Solution of Dirac equation and greybody radiation around a regular Bardeen black hole surrounded by quintessence

## TL;DR

This paper derives exact solutions to the Dirac equation around a regular Bardeen black hole with quintessence, analyzes the effects of quintessence on effective potentials, and studies greybody radiation of spin-0 particles.

## Contribution

It provides a new analytical approach to the Dirac equation in the BBHSQ background and examines the influence of quintessence on particle behavior and radiation.

## Key findings

- Effective potentials depend on quintessence parameters.
- Angular solutions are expressed in spherical harmonics.
- Greybody radiation characteristics are analyzed.

## Abstract

The exact solutions of the Dirac equation that describe a massive, non-charged particle with spin-(1/2) in the curved spacetime geometry of regular Bardeen black hole surrounded by quintessence (BBHSQ) are investigated. We first derive the Dirac equation in the BBHSQ background using a null tetrad in the Newman-Penrose formalism. Afterward, we separate the Dirac equation into ordinary differential equations for the radial and angular parts. The angular equations are solved exactly in terms of standard spherical harmonics. The radial part equations are transformed into a Schr\"odinger like differential wave equations with effective potentials. The effect of the quintessence on the regular Bardeen black hole is studied by understanding the physical behavior of the effective potentials. In addition, the potentials are plotted with changing the quintessence parameters, magnetic monopole charge parameter and the frequency of the particle in the physically acceptable regions. Finally, we study the greybody radiation of spin-0 particles from the BBHSQ.