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# New Developments in Relativistic Viscous Hydrodynamics

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### Abstract

Starting with a brief introduction into the basics of relativistic fluid dynamics, I discuss our current knowledge of a relativistic theory of fluid dynamics in the presence of (mostly shear) viscosity. Derivations based on the generalized second law of thermodynamics, kinetic theory, and a complete second-order gradient expansion are reviewed. The resulting fluid dynamic equations are shown to be consistent for all these derivations, when properly accounting for the respective region of applicability, and can be applied to both weakly and strongly coupled systems. In its modern formulation, relativistic viscous hydrodynamics can directly be solved numerically. This has been useful for the problem of ultrarelativistic heavy-ion collisions, and I will review the setup and results of a hydrodynamic description of experimental data for this case.

### Most cited references30

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### Ultraviolet Behavior of Non-Abelian Gauge Theories

(1973)
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### Highly relativistic nucleus-nucleus collisions: The central rapidity region

(1983)
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### Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics

(2004)
The ratio of shear viscosity to volume density of entropy can be used to characterize how close a given fluid is to being perfect. Using string theory methods, we show that this ratio is equal to a universal value of $$\hbar/4\pi k_B$$ for a large class of strongly interacting quantum field theories whose dual description involves black holes in anti--de Sitter space. We provide evidence that this value may serve as a lower bound for a wide class of systems, thus suggesting that black hole horizons are dual to the most ideal fluids.
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### Author and article information

###### Journal
20 February 2009
2009-10-12
0902.3663 10.1142/S0218301310014613

INT-PUB-09-010
Int.J.Mod.Phys.E19:1-53,2010
49 pages, 12 figures, lecture notes in review form; v2: added references; v3: typo in (40) corrected
hep-ph hep-th nucl-th