Does stability of relativistic dissipative fluid dynamics imply causality?

Abstract

We investigate the causality and stability of relativistic dissipative fluid dynamics in the absence of conserved charges. We perform a linear stability analysis in the rest frame of the fluid and find that the equations of relativistic dissipative fluid dynamics are always stable. We then perform a linear stability analysis in a Lorentz-boosted frame. Provided that the ratio of the relaxation time for the shear stress tensor, ${\tau }_{\pi }$, to the sound attenuation length, ${\Gamma }_s=4\eta /3(\epsilon +P)$, fulfills a certain asymptotic causality condition, the equations of motion give rise to stable solutions. Although the group velocity associated with perturbations may exceed the velocity of light in a certain finite range of wavenumbers, we demonstrate that this does not violate causality, as long as the asymptotic causality condition is fulfilled. Finally, we compute the characteristic velocities and show that they remain below the velocity of light if the ratio ${\tau }_{\pi }/{\Gamma }_s$ fulfills the asymptotic causality condition.

30 pages, 10 figures.

References in corpus (17)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Suppression of elliptic flow in a minimally viscous quark-gluon plasma
• Hydrodynamic Models for Heavy Ion Collisions
• Relativistic hydrodynamics for heavy-ion collisions
• Stability and Causality in relativistic dissipative hydrodynamics
• Viscous hydrodynamics relaxation time from AdS/CFT
• Relativistic Dissipative Hydrodynamics: A Minimal Causal Theory
• Dissipative effects from transport and viscous hydrodynamics
• Constraining relativistic viscous hydrodynamical evolution
• Shear viscosity coefficient and relaxation time of causal dissipative hydrodynamics in QCD
• Shock propagation and stability in causal dissipative hydrodynamics
• Formulating Viscous Hydrodynamics for Large Velocity Gradients
• Extensivity of Irreversible Current and Stability in Causal Dissipative Hydrodynamics
• Dissipative hydrodynamics and heavy ion collisions
• Aspects of causal viscous hydrodynamics

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