The Holtsmark distribution of forces and its role in gravitational clustering

Abstract

The evolution and the statistical properties of an infinite gravitating system represent an interesting and widely investigated subject of research. In cosmology, the standard approach is based on equations of hydrodynamics. In the present paper, we analyze the problem from a different perspective, which is usually neglected. We focus our attention on the fact that at small scale the distribution is point-like, or granular, and not fluid-like. The basic result is that the discrete nature of the system is a fundamental ingredient to understand its evolution. The initial configuration is a Poisson distribution in which the distribution of forces is governed by the Holtsmark function. Computer simulations show that the structure formation corresponds to the shift of the granularity from small to large scales. We also present a simple cellular automaton model that reproduces this phenomenon.