A covariant gravitational Landau equation for discreteness fluctuations

Starting from a relativistic Vlasov description for a system of stars that is not 'too relativistic', this paper examines the effects of ''discreteness'' fluctuations and shows that, in the limit that these may be associated with relatively proximate stars also it is shown that the average distribution function fo will satisfy the relativistic Landau equation. This alternative derivation of the Landau equation views ''discreteness'' effects as being only one particular type of fluctuation which one might envisage, and, as such, suggests the possibility of an effective relaxation induced by collective fluctuations, which has already been explored in the Newtonian limit. (author)