New Developments in Relativistic Viscous Hydrodynamics

TL;DR

This paper reviews the theoretical foundations and recent developments in relativistic viscous hydrodynamics, emphasizing its consistency, applicability to different systems, and successful numerical modeling of heavy-ion collision experiments.

Contribution

It provides a comprehensive review of derivations, consistency conditions, and applications of relativistic viscous hydrodynamics, highlighting recent advances and practical implementations.

Findings

Hydrodynamic equations are consistent across derivations when region of applicability is considered.

Relativistic viscous hydrodynamics can be numerically solved for complex systems.

Application to heavy-ion collisions successfully describes experimental data.

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.