The energy-momentum tensor in relativistic kinetic theory: the role of the center of mass velocity in the transport equations for multicomponent mixtures

TL;DR

This paper compares two relativistic kinetic theory frameworks for multicomponent mixtures, highlighting how the choice of center of mass velocity affects the structure of the energy-momentum tensor and the inclusion of heat and diffusion fluxes.

Contribution

It clarifies the role of the center of mass velocity in formulating the energy-momentum tensor in relativistic mixtures, contrasting Eckart and Landau-Lifshitz approaches.

Findings

Different definitions of center of mass velocity lead to distinct forms of the energy-momentum tensor.

In the particle/Eckart frame, heat is included in the energy-momentum tensor.

In the energy/Landau-Lifshitz frame, relativistic effects influence diffusion fluxes.

Abstract

Relativistic kinetic theory is applied to the study of the balance equations for relativistic multicomponent mixtures, comparing the approaches corresponding to Eckart's and Landau-Lifshitz's frames. It is shown that the concept of particle velocity relative to the center of mass of the fluid is essential to establish the structure of the energy-momentum tensor in both cases. Different operational definitions of the center of mass velocity lead either to the inclusion of heat in the energy-momentum tensor (particle/Eckart frame) or to strictly relativistic contributions to the diffusion fluxes (energy/Landau-Lifshitz frame). The results here obtained are discussed emphasizing the physical features regarding each approach.