The relativistic kinetic equation for gravitationally interacting particles

The authors derive the relativistic kinetic equation for the one-particle distribution function of gravitationally interacting particles to second order in the coupling constant. The interaction is described within the framework of general relativity. The kinetic equation for gravitationally interacting particles has a great deal in common with the Belyaev-Budker relativistic kinetic equation for plasma; the only difference consists of a change in a scalar factor that occurs in the kernel of the collision integral and depends on the momenta of the interacting particles. In the relativistic limit, the equation is the same as the equation derived by Bisnovatyi-Kogan and Shukham [Soviet Phys. JETP 55, 1 (1982)] for Newtonian gravitation. The authors discuss the application of the kinetic equation to a system containing two types of particles--nonrelativistic massive particles and ultrarelativistic massless particles