1307.2477 (Tomoi Koide et al.)

Bivelocity picture in the nonrelativistic limit of relativistic
hydrodynamics    [PDF]

Tomoi Koide, Rudnei O. Ramos, Gustavo S. Vicente

We discuss the nonrelativistic limit of relativistic hydrodynamics. The lowest order truncation of the velocity expansion leads to the Navier-Stokes-Fourier theory. However, when the next-to-leading order corrections are included, the equations can be expressed concurrently with two different fluid velocities; one parallel to the conserved charge current flow (which follows the Eckart definition) and the other parallel to the energy current flow (which follows the Landau-Lifshitz definition). We compare this next-to-leading order relativistic hydrodynamics with the bivelocity hydrodynamics, which is one of the generalizations of the Navier-Stokes-Fourier theory and is formulated such as 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. Thus, various assumptions that are introduced in the formulation of the bivelocity hydrodynamics are shown to be reproduced in the next-to-leading order relativistic hydrodynamics.

View original: http://arxiv.org/abs/1307.2477