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

TL;DR

This paper investigates the initial conditions of one-dimensional expanding viscous fluids in relativistic heavy-ion collisions, revealing causality constraints that limit the applicability of hydrodynamics and suggesting the need for non-equilibrium models.

Contribution

It introduces causality-based constraints on initial conditions in relativistic hydrodynamics, highlighting the limitations of hydrodynamic descriptions at early stages of heavy-ion collisions.

Findings

Causality conditions are violated at large deviations from local equilibrium.

Minimum initial proper time and maximum energy density are derived from causality constraints.

Hydrodynamics may not be valid at the earliest stages of heavy-ion collisions.

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.