Scalar self-energy for a charged particle in global monopole spacetime with a spherical boundary

TL;DR

This paper investigates how a global monopole's spacetime geometry combined with a spherical boundary affects the self-energy of a scalar charged particle, revealing boundary-dependent forces and stability conditions.

Contribution

It provides a detailed analysis of the scalar self-energy in a global monopole spacetime with a spherical boundary, including new Green function formulations and boundary condition effects.

Findings

Boundary-induced self-energy dominates near the sphere.

Self-force can be attractive or repulsive depending on boundary conditions.

Stable equilibrium points exist for certain boundary conditions and couplings.

Abstract

We analyze combined effects of the geometry produced by global monopole and a concentric spherical boundary on the self-energy of a point-like scalar charged test particle at rest. We assume that the boundary is outside the monopole's core with a general spherically symmetric inner structure. An important quantity to this analysis is the three-dimensional Green function associated with this system. For both Dirichlet and Neumann boundary conditions obeyed by the scalar field on the sphere, the Green function presents a structure that contains contributions due to the background geometry of the spacetime and the boundary. Consequently the corresponding induced scalar self-energy present also similar structure. For points near the sphere the boundary-induced part dominates and the self-force is repulsive/attractive with respect to the boundary for Dirichlet/Neumann boundary condition. In the region outside the sphere at large distances from it, the boundary-free part in the self-energy dominates and the corresponding self-force can be either attractive or repulsive with dependence of the curvature coupling parameter for scalar field. In particular, for the minimal coupling we show the presence of a stable equilibrium point for Dirichlet boundary condition. In the region inside the sphere the nature of the self-force depends on the specific model for the monopole's core. As illustrations of the general procedure adopted we shall consider two distinct models, namely flower-pot and the ballpoint-pen ones.