Ultrarelativistic transport coefficients in two dimensions

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-Juttner 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 previous results, it is found that the temperature dependence becomes the same as for the Anderson-Witting model.