Third-order relativistic dissipative fluid dynamics from the method of moments

Abstract

We derive a linearly causal and stable third-order relativistic fluid-dynamical theory from the Boltzmann equation using the method of moments. For this purpose, we demonstrate that such theory must include novel degrees of freedom, corresponding to irreducible tensors of rank 3 and 4. The equations of motion derived in this work are compared with numerical solutions of the Boltzmann equation, considering an ultrarelativistic, classical gas in the highly symmetric Bjorken flow scenario. These solutions are shown to be in good agreement for a wide range of values of shear viscosity and initial temperatures.