The state of a static spherically symmetric relativistic axionically active multi-component plasma in the gravitational, magnetic and electric fields of an axionic dyon is studied in the framework of the Einstein -Maxwell -Fermi -Dirac -axion theory. We assume that the equations of axion electrodynamics, the covariant relativistic kinetic equations, and the equation for the axion field with modified periodic and Higgs-type potentials are nonlinearly coupled; the gravitational field in the dyon exterior is assumed to be fixed and to be of the Reissner-Nordström type. We introduce the extended Lorentz force, which acts on the particles in the axionically active plasma, and analyze the consequences of this generalization. The analysis of exact solutions, obtained in the framework of this model for the relativistic Boltzmann electron-ion and electron-positron plasmas, as well as, for degenerated zero-temperature electron gas, shows that the phenomena of polarization and stratification can appear in plasma, attracting attention to the axionic analog of the known Pannekoek-Rosseland effect.

We consider the structure of halos of the axionic dark matter, which surround massive relativistic objects with static spherically symmetric gravitational field and monopole-type magneto-electric fields. We work with the model of pseudoscalar field with the extended periodic potential, which depends on additional arguments proportional to the moduli of the Killing vectors; in our approach they play the roles of model guiding functions. The covariant model of the axion field with this modified potential is equipped with the extended formalism of the Killing vector fields, which is established in analogy with the formalism of the Einstein-aether theory, based on the introduction of a unit timelike dynamic vector field. We study the equilibrium state of the axion field, for which the extended potential and its derivative vanish, and illustrate the established formalism by the analysis of two-level axionic dark matter profiles, for which the stage delimiters relate to the critical values of the modulus of the timelike Killing vector field.

We consider the magnetic monopole in the axionic dark matter environment (axionic dyon) in the framework of the Reissner-Nordström-de Sitter model. Our aim is to study the distribution of the pseudoscalar (axion) and electric fields near the so-called folds, which are characterized by the profiles with the central minimum, the barrier on the left, and the maximum on the right of this minimum. The electric field in the fold-like zones is shown to change the sign twice, i.e., the electric structure of the near zone of the axionic dyon contains the domain similar to a double electric layer. We have shown that the described fold-like structures in the profile of the gravitational potential, and in the profiles of the electric and axion fields can exist, when the value of the dyon mass belongs to the interval enclosed between two critical masses, which depend on the cosmological constant.