Post-Newtonian non-equilibrium kinetic theory

TL;DR

This paper develops post-Newtonian hydrodynamic equations for non-perfect fluids using a relativistic Boltzmann framework, extending classical kinetic theory to include relativistic corrections.

Contribution

It introduces a post-Newtonian kinetic theory framework for non-equilibrium fluids, deriving new hydrodynamic equations and distribution functions with relativistic effects.

Findings

Derived post-Newtonian energy-momentum tensor components.

Obtained hydrodynamic equations from a post-Newtonian transfer equation.

Reproduced Newtonian hydrodynamics in the non-relativistic limit.

Abstract

The post-Newtonian hydrodynamic equations for a non-perfect fluid are developed within the framework of a post-Newtonian Boltzmann equation. The post-Newtonian components of the energy-momentum tensor are determined by considering the relativistic Eckart decomposition for a viscous and heat conducting fluid. From the relativistic Grad distribution function its post-Newtonian expression is derived. The hydrodynamic equations for the mass density, mass-energy density and momentum density are determined from a post-Newtonian transfer equation and Grad's distribution function. In the non-relativistic limit the Newtonian hydrodynamic equations for mass, momentum and energy densities are recovered.