Analysis of eigenmodes in a relativistic gas

The eigenmodes of a relativistic gas within a five-, thirteen- and fourteen-field theories are analyzed in the ultra-relativistic, relativistic and non-relativistic regimes. The five-field theory furnishes one non-propagating and two propagating hydrodynamic modes and there appear sound propagation gaps caused by a coupling of thermal and pressure fluctuations at large wavenumbers. Apart from the three hydrodynamic modes of the five-field theory in the fourteen-field theory emerge more three kinetic sound modes, which at small wavenumbers are purely non-propagating diffusive modes. In the thirteen-field theory, there appear the three hydrodynamic of the five-field theory and two kinetic sound modes, which do not propagate for small values of the wavenumber. It is shown that the fourteen- and the thirteen-field theories exhibit no sound propagation gaps, so that these gaps are shortcomings that arise from the five-field theory.