2026/04/30 by Gilberto M. Kremer
Physics and Astronomy · #gr-qc
14 pages
arxiv created 2026/08/06 · arxiv updated 2026/08/07
Within the framework of the post-Newtonian 2\frac12 approximation theory, a kinetic theory for relativistic gases in the presence of gravitational fields is developed. The Boltzmann equation and the equilibrium Maxwell--Jüttner distribution function are determined up to 1/c7--order, which are used to calculate the components of the particle four-flow and energy-momentum tensor and to find the Eulerian hydrodynamic equations for the mass, mass-energy, and momentum densities in the 2\frac12--post-Newtonian approximation. The energy conservation law follows from the hydrodynamic equation for the total energy density, which is a combination of the hydrodynamic equations for the mass and the mass-energy densities. Here, the total energy conservation law is derived in the 1\frac12--post-Newtonan approximation, since we have to know the components of the metric tensor gij in the 3\frac12--th post-Newtonian approximation to obtain the energy conservation law in the 2\frac12--th post-Newtonian approximation.