Induced electrostatic self-interaction in the spacetime of a global monopole with inner structure

TL;DR

This paper investigates the electrostatic self-energy and self-force on a point charge in a global monopole spacetime with an inner structure, deriving exact expressions for these quantities inside and outside the monopole's core.

Contribution

It introduces a detailed analysis of self-interactions in a global monopole spacetime considering its inner structure, providing explicit Green function calculations and exact self-energy expressions.

Findings

Self-energy has two contributions: geometric and inner structure correction.

Exact self-energy expressions are obtained for regions inside and outside the monopole's core.

Inner structure influences the electrostatic self-interaction significantly.

Abstract

In this work we analise the electrostatic self-energy and self-force on a point-like electric charged particle induced by a global monopole spacetime considering a inner structure to it. In order to develop this analysis we calculate the three-dimensional Green function associated with this physical system. We explicitly show that for points inside and outside the monopole's core the self-energy presents two distinct contributions. The first is induced by the geometry associated with the spacetime under consideration, and the second one is a correction due to the non-vanishing inner structure attributed to it. Considering specifically the ballpoint-pen model for the region inside, we were able to obtain exact expressions for the self-energies in the regions outside and inside the monopole's core.