On the hydrodynamical description of waves in hot relativistic plasma

It is shown that using the energy - momentum tensor of material in the form T$^{ij}$= (ε+p)τ$^{i}$τ$^{j}$-g$^{ij}$p with wave emission in a relativistic plasma leads to incorrect dispersion of the plasma waves. A closed system of equations for relativistic plasma is constructed in the hydrodynamic approximation, taking the retardation of the radiation into account, and on this basis the dispersion and radiational - damping decrements of the wave are obtained, with results that do not contradict kinetic theory.