On the nature of gravitational forces

TL;DR

This paper investigates how inhomogeneity in particle distribution affects gravitational force statistics, showing that inhomogeneity enhances dynamical friction and aligns theoretical predictions with N-body simulation results.

Contribution

It extends the statistical analysis of gravitational forces to inhomogeneous systems and confirms the theoretical predictions with N-body simulations.

Findings

Inhomogeneity modifies the force distribution functions.

Dynamical friction is enhanced in inhomogeneous backgrounds.

Theoretical models agree well with simulation data.

Abstract

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