Effect of a cylindrical thin-shell of matter on the electrostatic self-force on a charge

TL;DR

This paper analyzes how a cylindrical thin-shell of matter influences the electrostatic self-force on a charge, revealing conditions for attraction or repulsion based on the shell's matter properties and providing a method to interpret self-forces in shell-containing space-times.

Contribution

It introduces a method to interpret the self-force on a charge in cylindrical shell space-times using an equivalent electric potential approach, applicable to various geometries including wormholes.

Findings

Charge is repelled by shells with negative extrinsic curvature.

Charge is attracted to shells with positive extrinsic curvature.

The total image charge depends on the shell's properties and geometry.

Abstract

The electrostatic self-force on a point charge in cylindrical thin-shell space-times is interpreted as the sum of a $bulk$ field and a $shell$ field. The $bulk$ part corresponds to a field sourced by the test charge placed in a space-time without the shell. The $shell$ field accounts for the discontinuity of the extrinsic curvature ${\kappa^p}_q$. An equivalent electric problem is stated, in which the effect of the shell of matter on the field is reconstructed with the electric potential produced by a non-gravitating charge distribution of total image charge $Q$, to interpret the shell field in both the interior and exterior regions of the space-time. The self-force on a point charge $q$ in a locally flat geometry with a cylindrical thin-shell of matter is calculated. The charge is repelled from the shell if ${\kappa^{p}}_{p}=\kappa<0$ (ordinary matter) and attracted toward the shell if $\kappa>0$ (exotic matter). The total image charge is zero for exterior problems, while for interior problems $Q/q=-\kappa \, r_e$, with $r_e$ the external radius of the shell. The procedure is general and can be applied to interpret self-forces in other space-times with shells, e.g., for locally flat wormholes we found $Q_{\mp}^{wh}/q=-1/ (\kappa_{wh} r_{\pm})$.