  The necessary and sufficient conditions for a perfect energy tensor to
describe the energy evolutions of a monoatomic relativistic Synge gas are
obtained. Then, a Rainich-like theory for the Einstein-Synge solutions can be
constructed. Equations of state approximating that of a Synge gas at low or at
high temperatures, or in the entire domain of applicability, are analyzed from
a hydrodynamic point of view.
