BRANS–DICKE AND RELATED EUCLIDEAN WORMHOLES

In a recent paper¹ Euclidean wormhole solution has been obtained with a vacuum Brans–Dicke theory with parameter ω=0. These wormholes suffer from unphysical values of the gravitational constant. One can relate the various known wormholes by means of conformal transformations; although one should not transform them directly to the Einstein frame as the gravitational constant there is "forced" physical: so removing the wormholes.

However, by arguing for the existence of a fundamental minimum length scale such wormholes can now be considered as representative of quantum gravitational phenomena. One can also obtain wormholes as solutions of the quantum mechanical Wheeler–De Witt equation; now in Brans–Dicke for any ω>-3/2.