Relativistic Eulerian rarefied gas with internal structure

Recently Pennisi and Ruggeri [Ann. Phys. 377, 414 (2017)] proposed a casual hyperbolic model for a dissipative relativistic gas with internal structure. In this paper, we consider the particular case of the model when dissipation is negligible (Eulerian gas). We study in particular the energy behavior in comparison with the Synge energy which is valid for monatomic gas and we evaluate the characteristic velocities proving the hyperbolicity of the differential system. The second part of the paper is devoted to the ultra-relativistic limit of the model and we prove that there exists a critical value of the degree of freedom such that for smaller values of this quantity the ultra-relativistic limit of the energy of a gas with structure is the same as the Synge energy, while for larger degrees of freedom the energy increases with the degree of freedom itself.