The influence of the gravitational field on remarkable phenomena in condensed matter physics appears to be a new and stimulating research field, both from the experimental and theoretical points of view. In particular, the occurrence and the eventual response of a Bose-Einstein condensates to the presence of a gravitational field is worthwhile to be investigated, as it can give rise to interesting and observable effects. It is also quite relevant to understand the role of the presence of localized impurities, which are always present in any realistic system, in the quantum dynamical mechanism which eventually allows the formation of a condensate.

As a matter of fact, it has been recently shown that an ideal boson gas in the absence of impurities does notcondense if a uniform gravitational field is present. We propose to investigate the existence and the main features of a Stark-like effect, which arises if an ideal boson gas is under the influence of a uniform gravitational field and of a point-like impurity in the non-relativistic one-, two- and three-dimensional cases. We shall also attempt to consider the cases of the presence of more than one point-like impurity as well as the possibility of a two-bodies interaction among the molecules of the boson gas.