Einstein–Maxwell-axion theory: dyon solution with regular electric field

In the framework of the Einstein–Maxwell-axion theory we consider static spherically symmetric solutions which describe a magnetic monopole in the axionic environment. These solutions are interpreted as the solutions for an axionic dyon, the electric charge of which is composite, i.e. in addition to the standard central electric charge it includes an effective electric charge induced by the axion–photon coupling. We focus on the analysis of those solutions which are characterized by the electric field regular at the center. Special attention is paid to the solutions with the electric field that is vanishing at the center, and that has the Coulombian asymptote, and thus displays an extremum at some distant sphere. Constraints on the electric and effective scalar charges of such an object are discussed.