# Integrability of the Dirac Equation on Backgrounds that are the Direct Product of Bidimensional Spaces

## TL;DR

This paper demonstrates the separability and integrability of the Dirac equation for spin 1/2 particles in certain higher-dimensional static black hole spacetimes with product topologies, facilitating solutions in these complex backgrounds.

## Contribution

It proves the separability of the Dirac equation in spacetimes that are direct products of 2D spaces, including specific black hole solutions with complex horizon topologies.

## Key findings

- Dirac equation is separable in these backgrounds.
- Separable solutions are obtained for certain static black holes.
- The results extend integrability to higher-dimensional spacetimes.

## Abstract

The field equation for a spin 1/2 massive charged particle propagating in spacetimes that are the direct product of 2-dimensional spaces is separated. Moreover, we use this result to attain the separability of the Dirac equation in some specific static black hole solutions whose horizons have topology $\mathbb{R}\times \mathbb{S}^2 \times \cdots \times \mathbb{S}^2$.