Kinetic and hydrodynamic post-Newtonian equations in the Brans–Dicke theory

A kinetic theory for the post-Newtonian Brans–Dicke theory is developed. The Boltzmann equation and the equilibrium Maxwell-Jüttner distribution function are determined from the knowledge of the components of the metric tensor and Christoffel symbols in the post-Newtonian Brans–Dicke theory. The hydrodynamic equations for the mass density, momentum density and mass-energy density are obtained from a transfer equation derived from the Boltzmann equation. The problem of self-gravitating fluid instabilities in the post-Newtonian Brans–Dicke theory is investigated.