The Energy-Momentum Tensor in Relativistic Kinetic Theory: The Role of the Center of Mass Velocity in the Transport Equations for Multicomponent Mixtures

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 energymomentum 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.

Landau and Eckart frames for relativistic fluids in nuclear collisions

“…There are two distinctive ways of defining the local rest frame for the flow: the Landau (or energy) frame [45] and the Eckart (or conserved charge/particle) frame [46]. There have been decades of debate over the eligibility of the two definitions of the local rest frame [20][21][22][23][24][47][48][49][50][51][52]. Most of the numerical analyses of hydrodynamic models for relativistic nuclear collisions so far do not give explicit consideration to the frame because the diffusion or the dissipation current is neglected, but the Landau frame is often considered to be a preferred choice when there is a theoretical need.…”