Non-Newtonian Properties of Relativistic Fluids
Abstract
We show that relativistic fluids behave as non-Newtonian fluids. First, we discuss the problem of acausal propagation in the diffusion equation and introduce the modified Maxwell-Cattaneo-Vernotte (MCV) equation. By using the modified MCV equation, we obtain the causal dissipative relativistic (CDR) fluid dynamics, where unphysical propagation with infinite velocity does not exist. We further show that the problems of the violation of causality and instability are intimately related, and the relativistic Navier-Stokes equation is inadequate as the theory of relativistic fluids. Finally, the new microscopic formula to calculate the transport coefficients of the CDR fluid dynamics is discussed. The result of the microscopic formula is consistent with that of the Boltzmann equation, i.e., Grad's moment method.
Keywords
Cite
@article{arxiv.1009.4643,
title = {Non-Newtonian Properties of Relativistic Fluids},
author = {Tomoi Koide},
journal= {arXiv preprint arXiv:1009.4643},
year = {2015}
}
Comments
16 pages, 10 figures, Invited Lecture at the Fourth Mexican Meeting on Mathematical and Experimental Physics, 19th to 23th July, 2010, El Colegio Nacional, M\'exico