1/r - Potential Without Charge

TL;DR

This paper explores the construction of wormholes in Reissner-Nordström spacetimes that generate electric field lines without actual charge, by identifying singular points and gluing spacetime regions at non-zero radii.

Contribution

It introduces a method to create charge-free electric fields via wormholes in complete Reissner-Nordström spacetimes, avoiding singularities at r=0.

Findings

Wormholes can generate electric fields without charge.

Gluing spacetimes at r>0 avoids singularities.

Surface energy tends to zero as r approaches zero.

Abstract

In order to get geodesically complete Reissner - Nordstroem space - times, it is necessary to identify pairs of singular points. This can be done in such a way that "wormholes" are created which generate electric field lines without any charge. Finally, it is shown that it is possible to glue these space - times not in the singularities r=0, but at some r>0. The surface energy generated by this gluing is exotic, but tends to zero in the limit r -> 0.