Post-Newtonian Kinetic Theory

Gilberto M. Kremer

doi:10.1016/j.aop.2021.168400

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arXiv · 2010.11017

Post-Newtonian Kinetic Theory

Gilberto M. Kremer

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Abstract

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.

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Gilberto M. Kremer. 2020-10-21. Post-Newtonian Kinetic Theory. https://doi.org/10.1016/j.aop.2021.168400

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