Determination of the Shear Viscosity Relaxation Time at Weak and Strong Coupling

Abstract

We investigate the microscopic origin of the relaxation time coefficient in relativistic fluid dynamics. We show that the extraction of the shear viscosity relaxation time via the gradient expansion is ambiguous and in general fails to give the correct result. The correct value for the shear viscosity relaxation time is extracted from the slowest non-hydrodynamic pole of the corresponding retarded Green's function, if such a pole is purely imaginary. According to the AdS/CFT correspondence, in strongly-coupled $\mathcal{N}=4$ SYM the non-hydrodynamic poles of the shear stress tensor nearest to the origin have a nonzero real part, which implies that the transient fluid-dynamical equations for this gauge theory are not equivalent to the well-known Israel-Stewart equations.

4 pages, To appear in the conference proceedings for Quark Matter 2011, May 23-28 2011, Annecy, France

References in corpus (4)

• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Dissipative relativistic fluid dynamics: a new way to derive the equations of motion from kinetic theory
• Stability and Causality in relativistic dissipative hydrodynamics
• Origin of the Relaxation Time in Dissipative Fluid Dynamics

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• The shear and bulk relaxation times from the general correlation functions