Hydrodynamic approach to the Synge gas
The relativistic Synge gas is the only relativistic fluid for which a macroscopic equation of state (EoS) has been obtained from microscopic kinetic theory. But Synge Eos involves modified Bessel functions and, therefore, it does not have a simple analytical expression. For this reason, different approximations have been considered in the literature in order to study the relativistic gas. In this paper, we obtain the necessary and sufficient conditions for a perfect energy tensor to describe the energy evolutions of a monoatomic relativistic Synge gas. We also analyze EoS approximating that of a Synge gas at low or at high temperatures, or in the entire domain of applicability, from a hydrodynamic point of view and propose some new ones.