Induced self-interactions in the spacetime of a global monopole with finite core

Abstract

In this paper we analyze induced self-interactions for point-like particles with electric and scalar charges placed at rest in the spacetime of a global monopole admitting a general spherically symmetric inner structure to it. In order to develop this analysis we calculate the three-dimensional Green function associated with the physical system under consideration. As we shall see for the charged particle outside the monopole core, the corresponding Green functions are composed by two distinct contributions, the firsts ones are induced by the non-trivial topology of the global monopole considered as a point-like defect and the seconds are corrections induced by the non-vanishing inner structure attributed to it. For both cases, the self-energies present a similar structure, having also two distinct contributions as well. For a specific model considered for region inside the monopole, named flower-pot, we shall see that the particle with electric charge will be always subject to a repulsive self-force with respect to the monopole core's boundary, on the other scalar charged particle exhibits peculiar behavior. Depending on the curvature coupling the self-force can be repulsive or attractive with respect to the core's boundary. Moreover, the contribution due to the point-like global monopole vanishes for massless particle conformally coupled with three dimensional space section of the manifold, and the only contribution comes from the core-induced part.