The relativistic configurations of systems of particles with a cutoff in their phase space distribution functions

Self-gravitating systems of classical particles with two distribution functions with different law of cutoff are considered: one corresponding to a truncated and one to a smoothed distribution. The results are compared and contrasted and large differences are found for low values of a suitably defined cutoff parameter. Some well known results due to Zel'dovich and Podurets are shown to be a consequence only of an arbitrary constraint imposed, by them, on the entire family of solutions.