2020/10/21 by Gilberto M. Kremer · 1 citation
Physics and Astronomy · #gr-qc #cond-mat.stat-mech
paper · pdf · doi:10.1016/j.aop.2021.168400
published as Annals of Physics 426 (2021) 168400 · 12 pages
arxiv created 2020/10/21 · arxiv updated 2021/02/04
A kinetic theory for relativistic gases in the presence of gravitational fields is developed in the second post-Newtonian approximation. The corresponding Boltzmann equation is determined from the evolution of the one-particle distribution function with respect to the proper time along the world line of the particle. From the knowledge of the equilibrium Maxwell-Jüttner distribution function in the second post-Newtonian approximation the components of the particle four-flow and energy-momentum tensor are obtained. The Eulerian hydrodynamic equations for the mass density, mass-energy density and momentum density in the second post-Newtonian approximation are determined from the Boltzmann equation. It is shown that the combination of the hydrodynamic equations of mass and mass-energy densities leads to the hydrodynamic equation for the internal energy density in the first post-Newtonian approximation.