Bivelocity picture in the nonrelativistic limit of relativistic hydrodynamics

TL;DR

This paper explores the nonrelativistic limit of relativistic hydrodynamics, revealing a bivelocity structure where two different fluid velocities emerge, corresponding to the Landau-Lifshitz and Eckart definitions, thus connecting relativistic corrections with bivelocity hydrodynamics.

Contribution

It demonstrates that the next-to-leading order relativistic corrections to the NFS theory naturally produce a bivelocity framework with velocities aligned to energy and charge currents.

Findings

Identification of the volume velocity with the Landau-Lifshitz velocity

Reproduction of bivelocity hydrodynamics structure in relativistic limit

Connection between relativistic corrections and bivelocity formulations

Abstract

We discuss the nonrelativistic limit of the relativistic Navier-Fourier-Stokes (NFS) theory. The next-to-leading order relativistic corrections to the NFS theory for the Landau-Lifshitz fluid are obtained. While the lowest order truncation of the velocity expansion leads to the usual NFS equations of nonrelativistic fluids, we show that when the next-to-leading order relativistic corrections are included, the equations can be expressed concurrently with two different fluid velocities. One of the fluid velocities is parallel to the conserved charge current (which follows the Eckart definition) and the other one is parallel to the energy current (which follows the Landau-Lifshitz definition). We compare this next-to-leading order relativistic hydrodynamics with bivelocity hydrodynamics, which is one of the generalizations of the NFS theory and is formulated in such a way to include the usual mass velocity and also a new velocity, called the volume velocity. We find that the volume velocity can be identified with the velocity obtained in the Landau-Lifshitz definition. Then, the structure of bivelocity hydrodynamics, which is derived using various nontrivial assumptions, is reproduced in the NFS theory including the next-to-leading order relativistic corrections.