Relativistic Boltzmann Theory and the Grad Method of Moments

Abstract

It has been the custom, when writing on relativistic Boltzmann theory, to justify such studies by recounting the various physical systems to which they can apply. By now one is sufficiently acquainted with relativistic plasmas, massive stellar systems and the like to make such justifications unnecessary. While applicability is of course the final justification for any physical theory, there is one other that I would like to mention briefly. It is the aesthetic appeal, so often emphasized by Dirac. The relativistic Boltzmann equation is both simple and elegant. From it one can obtain many beautiful results, such as those of Ehlers, Gerun and Sachs. It brings into play virtually the whole of relativity theory in one way or another and is amenable to analysis by such modern mathematical techniques as fiber bundle theory. It also affords a unifying view that is lacking in the classical theory, One need only compare the classical and relativistic treatments of radiative transfer theory, which is a special application of the Boltzmann equation to zero rest-mass particles to appreciate this fact. Finally I would mention that, even in the more mundane matter of finding approximate solutions, there are decided advantages to a relativistic treatment over the corresponding classical treatment.