Propagation speeds of relativistic conformal fluids from a generalized relaxation time approximation

TL;DR

This paper derives propagation speeds of relativistic conformal fluids from a kinetic theory approach with a generalized relaxation time, revealing how different relaxation time dependencies affect wave speeds.

Contribution

It introduces a parameterized distribution function and derives hydrodynamic equations to analyze wave propagation in relativistic fluids with arbitrary relaxation time functions.

Findings

Relaxation time form influences propagation speeds.

Anderson-Witting case ($a=1$) yields fastest speeds.

Derived speeds for scalar, vector, tensor perturbations.

Abstract

We compute the propagation speeds for a conformal real relativistic fluid. We begin from a kinetic equation in the relaxation time approximation, where the relaxation time is an arbitrary function of the particle energy in the Landau frame. We propose a parameterization of the one particle distribution function designed to contain a second order Chapman-Enskog solution as a particular case. We derive the hydrodynamic equations applying the moments method to this parameterized one particle distribution function, and solve for the propagation speeds of linearized scalar, vector and tensor perturbations. For relaxation times of the form $\tau=\tau_0(-\beta_{\mu}p^{\mu})^{-a}$, with $-\infty< a<2$, where $\beta_{\mu}=u_{\mu}/T$ is the temperature vector in the Landau frame, we show that the Anderson-Witting prescription $a=1$ yields the fastest speeds.