Existence and stability of shock waves in relativistic hydrodynamics with general equation of state

Different forms of criteria for the existence and stability of relativistic shock waves are compared. In case of a single-valued shock adiabat expressed as a function of pressure the requirement of the existence of a shock viscous profile is shown to be most restrictive. This criterion overlaps evolutionarity conditions, the entropy criterion and corrugation stability. The relativistic criterion of the spontaneous radiation of sound is proved to be equivalent to the condition of shock quasi-instability with respect to three-wave branching. The results are qualitatively analogous to those of a non-relativistic consideration.