Generalized Relativistic Chapman-Enskog Solution of the Boltzmann Equation

TL;DR

This paper extends the Chapman-Enskog method to relativistic kinetic theory, incorporating a time-derivative term linked to thermodynamic forces, with proofs of existence and uniqueness, and discusses heat transfer in relativity.

Contribution

It introduces a generalized relativistic Chapman-Enskog solution including a time-derivative term, expanding the mathematical framework of relativistic kinetic theory.

Findings

Proved existence and uniqueness of the generalized solution.

Analyzed the nature of heat as chaotic energy transfer in relativity.

Discussed mathematical implications of the generalization.

Abstract

The Chapman-Enskog method of solution of the relativistic Boltzmann equation is generalized in order to admit a time-derivative term associated to a thermodynamic force in its first order solution. Both existence and uniqueness of such a solution are proved based on the standard theory of integral equations. The mathematical implications of the generalization here introduced are thoroughly discussed regarding the nature of heat as chaotic energy transfer in the context of relativity theory.