Non-Newtonian Properties of Relativistic Fluids

TL;DR

This paper demonstrates that relativistic fluids exhibit non-Newtonian behavior and introduces a causal dissipative fluid dynamics framework using a modified Maxwell-Cattaneo-Vernotte equation, addressing causality and stability issues.

Contribution

It presents a new causal relativistic fluid dynamics model and a microscopic formula for transport coefficients consistent with Boltzmann equation results.

Findings

Relativistic fluids behave as non-Newtonian fluids.

The modified MCV equation ensures causality in relativistic fluid dynamics.

The microscopic formula aligns with Boltzmann and Grad's methods.

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.