Gravitational force distribution in fractal structures

We study the (Newtonian) gravitational force distribution arising from a fractal set of sources. We show that, in the case of real structures in finite samples, an important role is played by morphological properties and finite-size effects. For dimensions smaller than d − 1 (being d the space dimension) the convergence of the net gravitational force is assured by the fast decaying of the density, while for fractal dimension D > d − 1 the morphological properties of the structure determine the eventual convergence of the force as a function of distance. We clarify the role played by the cut-offs of the distribution. Some cosmological implications are discussed.