Electrostatics in a simple wormhole revisited

TL;DR

This paper revisits electrostatics in a simple wormhole, providing series and closed-form solutions for the potential, analyzing the influence of symmetry, and calculating self-energy and self-force for various cases.

Contribution

It offers a comprehensive analysis of electrostatic potentials in a simple wormhole, including solutions, symmetry considerations, and self-force calculations, advancing understanding in this theoretical context.

Findings

Potential depends on an arbitrary parameter in the general case.

Z2-symmetry fully determines the electrostatic potential.

Self-energy and self-force are explicitly calculated for different scenarios.

Abstract

The electrostatic potential generated by a point charge at rest in a simple static, spherically symmetric wormhole is given in the form of series of multipoles and in closed form. The general potential which is physically acceptable depends on a parameter due to the fact that the monopole solution is arbitrary. When the wormhole has Z2-symmetry, the potential is completely determined. The calculation of the electrostatic self-energy and of the self-force is performed in all cases considered.