The Holtsmark distribution of forces and its role in gravitational clustering

Abstract

The evolution and the statistical properties of an infinitegravitating system represent an interesting and widely investigated subject of research. In cosmology, the standardapproach is based on equations of hydrodynamics. In this paper, we analyse the problem from a different perspective,which is usually neglected. We focus our attention on the factthat at small scale the distribution is point-like, or granular,and not fluid-like. The basic result is that the discrete natureof the system is a fundamental ingredient in understanding itsevolution. The initial configuration is a Poisson distributionin which the distribution of forces is governed by the Holtsmarkfunction. Computer simulations show that the structure formationcorresponds to the shift of the granularity from small to largescales. We also present a simple cellular automaton model thatreproduces this phenomenon.