Universality classes of relativistic fluid dynamics: Applications

Using a formalism that was recently developed in a companion Letter, we rigorously prove the equivalence, in the linear regime, of a number of apparently different relativistic hydrodynamic theories proposed in the literature. In particular, we show that $\mathrm{Hydro}+$ is indistinguishable from the Israel-Stewart theory for bulk viscosity, which in turn is indistinguishable from a reacting mixture. The two-fluid model for superfluidity coincides with the Israel-Stewart theory for heat conduction in the limit of infinite conductivity, and this explains why the latter has a second sound. Also, ${\mathrm{MIS}}^{*}$ is equivalent to the Burgers model for viscoelasticity, and this implies that the former must exhibit an elastic behavior at high frequencies. Additionally, we show that if the degrees of freedom and the conservation laws of a hydrodynamic theory have the same geometric character as those of the Israel-Stewart theory, then such theory must be indistinguishable from the Israel-Stewart theory in the linear regime. This explains why all second-order theories turn out to be identical near equilibrium. Finally, we construct the first linearized model, to our knowledge, for a relativistic supersolid that is proven to be causal, stable, and strongly hyperbolic.