Decay and Subluminality of Modes of all Wave Numbers in the Relativistic Dynamics of Viscous and Heat Conductive Fluids

TL;DR

This paper analytically confirms that all wave modes in a relativistic viscous and heat-conductive fluid model decay over time and travel below the speed of light, ensuring causality and stability across all wave numbers and frames.

Contribution

It provides the first fully analytical proof of subluminal and decaying modes for all wave numbers in a five-field relativistic dissipative fluid model.

Findings

All Fourier-Laplace modes decay over time.

Modes travel at subluminal speeds.

Properties hold in arbitrary Lorentz frames.

Abstract

To further confirm the causality and stability of a second-order hyperbolic system of partial differential equations that models the relativistic dynamics of barotropic fluids with viscosity and heat conduction (H. Freist\"uhler and B. Temple, J. Math. Phys. 59 (2018)), this paper studies the Fourier-Laplace modes of this system and shows that all such modes, relative to arbitrary Lorentz frames, (a) decay with increasing time and (b) travel at subluminal speeds. Stability is also shown for the related model of non-barotropic fluids (H. Freist\"uhler and B. Temple. Proc. R. Soc. A 470 (2014) and Proc. R. Soc. A 473 (2017)). Even though these properties had been known for a while in the sense of numerical evidence, the fully analytical proofs for the subluminality of modes of arbitrary wave numbers in arbitrary frames given here appear to be the first regarding any five-field formulation of dissipative relativistic fluid dynamics.