Electrostatic interaction of a pointlike charge with a wormhole

TL;DR

This paper analyzes the electrostatic potential of a point charge near a wormhole, revealing a self-force due to the wormhole's topology and interpreting flux as a wormhole charge, differing from previous results.

Contribution

It provides an explicit calculation of the self-force on a charge near a wormhole and interprets the flux as a wormhole charge, extending Wheeler's concept.

Findings

The potential differs from Coulomb's law near the wormhole.

A self-force acts on the charge even without source-free fields.

Flux through the wormhole relates to the wormhole's effective charge.

Abstract

A pointlike electric charge at rest is considered in the spacetime which is a wormhole connecting two otherwise Minkowskian spaces. The potential (i. e. a solution of the Maxwell equations) is split into two parts: one of them depends only on the value and location of the charge, while the other, on the contrary, does not change when the charge is quasistatically moved. Correspondingly, the former is interpreted as being generated by the charge, and the latter as being source-free. It is shown that all source-free potentials differ in the flux through the throat (no "multipoles without multipoles"), which enables one to interpret the flux as the "charge" of the wormhole in agreement with Wheeler's concept of "charge without charge". The potential generated by the charge differs from Coulomb's and thus a force (called "self-force") acts on the charge even in the absence of the source-free field. This force is found explicitly in the limit of vanishing throat length. The result differs from that obtained recently by Khusnutdinov and Bakhmatov.