Geometric Dilaton Coupling and Smooth Charged Wormholes

TL;DR

This paper introduces a geometric interpretation of a dilaton coupling that yields smooth, wormhole-like solutions for magnetic cases, while electric solutions remain singular unless an alternative coupling is used.

Contribution

It presents a novel geometric interpretation of dilaton coupling and derives new smooth wormhole solutions for magnetic charges, contrasting with singular electric solutions.

Findings

Magnetic solutions are smooth and geodesically complete wormholes.

Electric solutions are singular and incomplete under the original coupling.

An alternative coupling allows smooth electric solutions.

Abstract

A particular type of coupling of the dilaton field to the metric is shown to admit a simple geometric interpretation in terms of a volume element density independent from the metric. For dimension n = 4 two families of either magnetically or electrically charged static spherically symmetric solutions to the Maxwell-Einstein-Dilaton field equations are derived. Whereas the metrics of the "magnetic" spacetimes are smooth, geodesically complete and have the topology of a wormhole, the "electric" metrics behave similarly as the singular and geodesically incomplete classical Reissner-Nordstroem metrics. At the price of losing the simple geometric interpretation, a closely related "alternative" dilaton coupling can nevertheless be defined, admitting as solutions smooth "electric" metrics.