Does stability of relativistic dissipative fluid dynamics imply causality?

Journal Article · Tue Jun 01 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.81.114039· OSTI ID:21407984

Pu, Shi ^[1]; Koide, Tomoi ^[2]; Rischke, Dirk H ^[1]

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1. Institut fuer Theoretische Physik, Johann Wolfgang Goethe-Universitaet, Max-von-Laue-Strasse 1, D-60438 Frankfurt am Main (Germany)
2. Frankfurt Institute for Advanced Studies, Ruth-Moufang-Strasse 1, D-60438 Frankfurt am Main (Germany)

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}{sub {pi}}to the sound attenuation length {Gamma}{sub 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 wave numbers, 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}{sub {pi}/{Gamma}s} fulfills the asymptotic causality condition.

• OSTI ID: 21407984
• Journal Information: Physical Review. D, Particles Fields, Vol. 81, Issue 11; Other Information: DOI: 10.1103/PhysRevD.81.114039; (c) 2010 The American Physical Society; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ASYMPTOTIC SOLUTIONS
DISTURBANCES
EQUATIONS OF MOTION
FLUID MECHANICS
FLUIDS
PERTURBATION THEORY
RELATIVISTIC RANGE
RELAXATION TIME
STABILITY
DIFFERENTIAL EQUATIONS
ENERGY RANGE
EQUATIONS
MATHEMATICAL SOLUTIONS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS