Constraint on initial conditions of one-dimensional expanding fluids from nonlinear causality

Abstract

The initial conditions of one-dimensional expanding viscous fluids in relativistic heavy-ion collisions are scrutinized in terms of nonlinear causality of the relativistic hydrodynamic equations. Conventionally, it is believed that the matter generated in relativistic heavy-ion collisions starts to behave as a fluid all at once at some initial time. However, it is by no means trivial how soon after the first contact of two high-energy nuclei the fluid picture can be applied. It is demonstrated that one-dimensional expanding viscous fluids violate the necessary and the sufficient conditions of nonlinear causality at large departures from local equilibrium. We therefore quantify the inverse Reynolds number to justify the hydrodynamic description to be valid. The initial conditions are strictly constrained not to violate the causality conditions during the time evolution. With the help of the transverse energies per rapidity measured at RHIC and LHC, we obtain the minimum initial proper time and the maximum energy density allowed by nonlinear causality. This analysis strongly suggests that the initial stage of relativistic heavy-ion collisions needs to be described by a non-equilibrium description other than the framework of relativistic dissipative hydrodynamics.