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

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 $\mathbb{R}\times {\mathbb{S}}^2\times \cdots \times {\mathbb{S}}^2$.