New application of the Killing vector field formalism: modified periodic potential and two-level profiles of the axionic dark matter distribution

Abstract

© 2020, The Author(s). 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.