Abstract

Kinetic and hydrodynamic models describing early stages of relativistic heavy-ion collisions are discussed. We emphasise the role of the shear-bulk coupling for the correct determination of the time dependence of the bulk viscous pressure.

Highlights

  • Relativistic hydrodynamics plays an important role in modeling of relativistic heavy-ion collisions [1,2,3,4,5,6,7,8,9,10,11,12,13]

  • We argue that the improved description of dissipative processes can be achieved if one uses either the complete second-order approaches or anisotropic hydrodynamics

  • We show that anisotropic hydrodynamics (aHydro) describes the evolution of the bulk pressure much better than the dissipative hydrodynamics based on Eqs. (7), (8), or (9)

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Summary

Introduction

Relativistic hydrodynamics plays an important role in modeling of relativistic heavy-ion collisions [1,2,3,4,5,6,7,8,9,10,11,12,13]. In this note we analyse simple models describing the early stages of relativistic heavy-ion collisions and point out difficulties one may encounter in the application of dissipative hydrodynamics [16]. We connect these problems with an incomplete character of various computational schemes which are used to derive the viscous hydrodynamic equations. [17, 18] we studied the effects connected with the shear viscosity and showed that recent formulations of second-order viscous hydrodynamics [20] agree better with the exact solutions of the kinetic equation than the standard Israel-Stewart approach [1, 2].

Dissipative and anisotropic hydrodynamics
Kinetic equation for boost-invariant and transversally homogenous systems
Bulk viscous pressure in dissipative and anisotropic hydrodynamics
Conclusions
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