Geometric dilaton gravity and smooth charged wormholes

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 corresponding Maxwell-Einstein-dilaton field equations are derived. Whereas the metrics of the 'magnetic' spacetimes are smooth, asymptotically flat, 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