  Solutions of the field equations of theories of gravity which admit distinct
conformal frame representations can look very different in these frames. We
show that Brans class IV solutions describe wormholes in the Jordan frame (in a
certain parameter range) but correspond to horizonless geometries in the
Einstein frame. The reasons for such a change of behaviour under conformal
mappings are elucidated in general, using Brans IV solutions as an example.
