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 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–Nordström 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.