Abstract
New formulations of relativistic dissipative hydrodynamics are discussed in the context of possible applications to describe early stages of relativistic heavy-ion collisions. The efficacy of different approaches is tested by making comparisons with the exact solutions of the kinetic equation.
Highlights
Relativistic viscous hydrodynamics [1,2,3,4,5,6,7,8,9,10,11,12,13] is the main building block in the standard model of relativistic heavyion collisions, which includes three important parts: the modeling of initial conditions, the application of relativistic hydrodynamics to describe the space-time evolution of matter, and, the modeling of the freeze-out conditions
The recent methods applied to improve the ae-mail: Wojciech.Florkowski@ifj.edu.pl efficacy of the more traditional hydrodynamic approaches include complete second-order treatments [27] and thirdorder treatments [28,29,30], In this note we discuss the applications of standard viscous hydrodynamics and anisotropic hydrodynamics in the context of the exact solutions of the Boltzmann kinetic equation [31,32,33]
We studied the effects connected with the shear viscosity and showed that recent formulations of second-order viscous hydrodynamics [27] agree better with the exact solutions of the kinetic equation than the standard Israel-Stewart approach [1, 2]
Summary
Relativistic viscous hydrodynamics [1,2,3,4,5,6,7,8,9,10,11,12,13] is the main building block in the standard model of relativistic heavyion collisions, which includes three important parts: the modeling of initial conditions, the application of relativistic hydrodynamics to describe the space-time evolution of matter, and, the modeling of the freeze-out conditions. The inclusion of viscous effects is important as it improves the overall description of the data (as compared to earlier perfect-fluid applications) and makes the applied theory consistent with general physics arguments that the fluid viscosity cannot be zero [14, 15]. The standard viscous hydrodynamics relies on the expansion around the local equilibrium state. This expansion may be questioned at the very early stages of relativistic heavy-ion collisions where the space-time gradients are large and the viscous corrections become very substantial in spite of the fact that the ratio of the shear viscosity to entropy density is minimal, η/s ∼ 1/(4π) [15]. It has been demonstrated that the correct description of the bulk viscous pressure demands the correct treatment of the bulk-viscous coupling [36, 37]
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