On the nature of gravitational forces

Abstract

In this paper, we will show how the statistics of the gravitational field is changed when the system is characterized by a non-uniform distribution of particles. We will show how the distribution functions W(F) and W(F,dF/dt), giving the joint probability that a test particle is subject to a force F and an associated rate of change of F given by dF/dt, are modified by inhomogeneity. Then we will calculate the first moment of dF/dt to study the effects of inhomogenity on dynamical friction. Finally we will test, by N-Body simulations, that the theoretical W(F) and dF/dt describes correctly the experimental data and we find that the stochastic force distribution obtained for the evolved system is in good agreement with theory. Moreover, we find that in an inhomogeneous background, the friction force is actually enhanced relative to the homogeneous case.