Thermodynamics and orientational order in systems of extended gravitating objects: A mean-field theory approach. I - Basic formalism

Abstract

A mean-field-theory approach, in which the orientation of an extended gravitating object is approximately determined by the mean gravitational field of all the other objects in the system, is presented. It is shown that the mean field is characterized by an effective single-body potential called the 'pseudopotential' which is obtained from the full two-body gravitational potential by means of a certain averaging procedure. The possible occurrence of an 'orientational phase transition' whereby large-scale orientational order may develop in the system is discussed.