Nonminimal dyons with regular gravitational, electric and axion fields

Abstract

We consider the distribution of the axionic dark matter and the profiles of the axionically induced electric field on the background of a regular magnetic monopole. The background static spherically symmetric spacetime is considered to be regular at the center of the object; it has no event horizons, the nonminimal interaction of strong gravitational and monopole type magnetic fields being the source of this regularity. We assume the pseudoscalar (axion) field to be nonminimally coupled to the electromagnetic and gravitational fields, and we search for solutions to the extended equations of nonminimal axion electrostatics, which satisfy two requirements: first, the axionically induced radial electric field vanishes at the center; second, the pseudoscalar field is regular at the center of the formed axionic dyon. We have found the set of parameters, describing the nonminimal axion-photon coupling, for which both requirements are satisfied. Properties of the two-parameter family of regular solutions to the equations of nonminimal axion electrostatics are analyzed numerically. The regular axionically induced electric field is shown to have the structure, which is typical for a simple electric layer.