  We present two formulations of Fokker-Planck-Rosenbluth-type (FPR) equations
for many-particle self-gravitating systems, with first order relativistic
corrections in the post-Newtonian approach (1PN). The first starts from a
covariant Fokker-Planck equation for a simple gas, introduced recently by G.
Chacon-Acosta and G. Kremer (Phys. Rev. E 76, 021201, 2007). The second
derivation is based on the establishment of an 1PN-BBGKY hierarchy, developed
systematically from the 1PN microscopic law of force and using the
Klimontovich-Dupree (KD) method. We close the hierarchy by the introduction of
a two-point correlation function that describes adequately the relaxation
process. This picture reveals an aspect that is not considered in the first
formulation: the contribution of ternary correlation patterns to the diffusion
coefficients, as a consequence of the nature of 1PN interaction. Both
formulations can be considered as a generalization of the equation derived by
Rezania and Sobouti (Astron. Astrophys. 54, 1110-1114, 2000), to stellar
systems where the relativistic effects of gravitation play a significant role.
