Fermionic fields in a four-dimensional $\Lambda$ Bonnor–Melvin space–time

We investigate how the gravitational field generated by a four-dimensional electrovacuum cosmological space–time influences the dynamics of fermionic fields governed by the Dirac equation, while also considering the effects of topology. We derive the radial wave equation corresponding to the relativistic Dirac equation and obtain analytical solutions for the energy levels and wave functions of the fermionic field within our framework. Our analysis reveals that various parameters, including the cosmological constant, the parameter responsible for space topology, and quantum numbers, play significant roles in determining the eigenvalues of the quantum particles. Specifically, we demonstrate that the presence of the topological parameter disrupts the degeneracy of the energy spectrum.