Boltzmann equation in the $2{\frac12}$-post-Newtonian approximation

Gilberto M. Kremer

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arXiv · 2604.27575

Boltzmann equation in the $2{\frac12}$-post-Newtonian approximation

Gilberto M. Kremer

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Abstract

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--J\"uttner distribution function are determined up to $1/c^7$--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 $g_{ij}$ in the $3\frac12$--th post-Newtonian approximation to obtain the energy conservation law in the $2\frac12$--th post-Newtonian approximation.

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Gilberto M. Kremer. 2026-04-30. Boltzmann equation in the $2{\frac12}$-post-Newtonian approximation. https://arxiv.org/abs/2604.27575

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