A monopole solution in Poincaré gauge theory

Summary

A special model of Poincaré gauge theory is considered, in which the theory can be thought of as the complex Yang-Mills theory on Einstein’s space-time. The Lorentz gauge field is then interpreted as a pair of fields: the «Yang-Mills» field and its partner: just like a pair of electric and magnetic fields. In this viewpoint, the possible existence of a monopole solution is investigated for the Lorentz gauge field in vacuum (no matter) which is assumed from the outset to be static and radially symmetric. The investigation is performed in a flat space-time approximation. As a result, we find a solution. Applying Kalb’s ansatz to the «Yang-Mills» equation, we see that the Yang-Mills part of the solution expresses «electric» and «magnetic» fields which are created by a point source with a unit «magnetic» charge and a certain «electric» charge. We find also that it is similar to one of those given by Morris and Carmeli. On the other hand, it is indicated that the partner field cannot create «Yang-Mills» partners in this solution just as an electric field cannot generate any magnetic field in a static limit.