Aspects of localized gravity around the soft minima

n-dimensional pure gravity theory can be obtained as the effective theory of an n+1 model (with noncompact extra dimension) where general n+1 reparametrization invariance is explicitly broken in the extra dimension. As was pointed out in the literature, a necessary consistency condition for having a nonvanishing four-dimensional Newton constant is the normalizability in the extra dimension of the zero mass graviton. This, in turn, implies that gravity localization is produced around the local minima of a potential in the extra dimension. We study gravity in the neighborhood of the soft (“thick”) local minima.