Novel Relaxation Time Approximation to the Relativistic Boltzmann Equation

We show that the widely used relaxation time approximation to the relativistic Boltzmann equation contains basic flaws, being incompatible with micro- and macroscopic conservation laws if the relaxation time depends on energy or general matching conditions are applied. We propose a new approximation that fixes such fundamental issues and maintains the basic properties of the linearized Boltzmann collision operator. We show how this correction affects transport coefficients, such as the bulk viscosity and particle diffusion.

Figure 1

Dimensionless bulk viscosity coefficient $\zeta /[t_R(ϵ+P)]$ as a function of $m\beta$, assuming Landau matching conditions. The results are shown for $\gamma =0$ (solid curve), $\gamma =0.5$ (dashed curve), and $\gamma =1$ (dash-dotted curve).

Figure 2

Dimensionless particle diffusion coefficient ${\kappa }_n/(t_{R}n)$ as a function of $m\beta$, assuming Landau matching conditions. The results are shown for $\gamma =0$ (solid curve), $\gamma =0.5$ (dashed curve), and $\gamma =1$ (dash-dotted curve).