Gravitational force distribution in fractal structures

Abstract

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.

9 pages, latex, 2 postscript figures, also available at http://www.phys.uniroma1.it/DOCS/PIL/pil.html Accepted for Publication in Europhysics Letters. Minor modifications added

References in corpus (1)

• The fractal structure of the universe : a new field theory approach

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