Ultrarelativistic Transport Coefficients in Two Dimensions

TL;DR

This paper calculates transport coefficients like shear and bulk viscosities and thermal conductivity for an ultrarelativistic fluid in 2+1 dimensions using the relativistic Boltzmann equation with two different relaxation time models, analyzing their temperature dependencies.

Contribution

It compares two relaxation time approximations for the relativistic Boltzmann equation and shows how modifications can unify their temperature dependence of transport coefficients.

Findings

Different temperature dependencies for the two models before modification.

Modified Marle model matches Anderson-Witting model's temperature dependence.

Transport coefficients depend linearly or quadratically on temperature depending on the model.

Abstract

We compute the shear and bulk viscosities, as well as the thermal conductivity of an ultrarelativistic fluid obeying the relativistic Boltzmann equation in 2+1 space-time dimensions. The relativistic Boltzmann equation is taken in the single relaxation time approximation, based on two approaches, the first, due to Marle and using the Eckart decomposition, and the second, proposed by Anderson and Witting and using the Landau-Lifshitz decomposition. In both cases, the local equilibrium is given by a Maxwell-Juettner distribution. It is shown that, apart from slightly different numerical prefactors, the two models lead to a different dependence of the transport coefficients on the fluid temperature, quadratic and linear, for the case of Marle and Anderson-Witting, respectively. However, by modifying the Marle model according to the prescriptions given in Ref.[1], it is found that the temperature dependence becomes the same as for the Anderson-Witting model.