Stability and causality in dissipative relativistic fluids

Hiscock, William A.; Lindblom, Lee

doi:10.1016/0003-4916(83)90288-9

Cited by 609 publications

(788 citation statements)

References 7 publications

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“…More specifically, we verified that the linearized equation of motion for small perturbations in the homogeneous, static background coincides with Hiscock-Lindblom [32][33][34] except for the coupling among the different irreversible currents. These couplings are not included in our theory considering the Curie principle.…”

Section: Summary and Concluding Remarkssupporting

confidence: 55%

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Causal theory of relativistic dissipative hydrodynamics

Denicol¹,

Kodama²,

Koide³

et al. 2007

Braz. J. Phys.

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We present a new formalism for the theory of relativistic dissipative hydrodynamics, where covariance and causality are satisfied by introducing the memory effect in irreversible currents. Our theory has a much simpler structure and thus has several advantages for practical purposes compared to the Israel-Stewart theory (IS). We apply our formalism to the Bjorken model and the results are shown to be analogous to the IS.

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Section: Summary and Concluding Remarkssupporting

confidence: 55%

“…Therefore we can easily see that our linearized equation of motion has the same structure as the IS with α 0 = α 1 = 0 . Thus the speed of pulse propagation is finite as discussed by Hiscock-Lindblom [32][33][34].…”

Section: Relativistic Dissipative Hydrodynamicsmentioning

confidence: 99%

Causal theory of relativistic dissipative hydrodynamics

Denicol¹,

Kodama²,

Koide³

et al. 2007

Braz. J. Phys.

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“…The numerical solution of (29), (30), and the total energy perturbation given by (26),ε = 1 +ε 1 +ε 2 , are shown in Fig. 2.…”

Section: A Soliton Initial Profilementioning

confidence: 99%

Nonlinear waves in second order conformal hydrodynamics

et al. 2015

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In this work we study wave propagation in dissipative relativistic fluids described by a simplified set of the 2nd order viscous conformal hydrodynamic equations corresponding to Israel-Stewart theory. Small amplitude waves are studied within the linearization approximation while waves with large amplitude are investigated using the reductive perturbation method, which is generalized to the case of 2nd order relativistic hydrodynamics. Our results indicate the presence of a "soliton-like" wave solution in Israel-Stewart hydrodynamics despite the presence of dissipation and relaxation effects.

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“…They are not completely arbitrary but related to c 2 b , the square of the velocity at which a viscous perturbation propagates [28] (see also [11]):…”

Section: Dynamics Of the Viscous Fluidmentioning

confidence: 99%

Bulk viscous cosmology with causal transport theory

Piattella

Fabris

Zimdahl

2011

J. Cosmol. Astropart. Phys.

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Abstract. We consider cosmological scenarios originating from a single imperfect fluid with bulk viscosity and apply Eckart's and both the full and the truncated Müller-Israel-Stewart's theories as descriptions of the non-equilibrium processes. Our principal objective is to investigate if the dynamical properties of Dark Matter and Dark Energy can be described by a single viscous fluid and how such description changes when a causal theory (Müller-IsraelStewart's, both in its full and truncated forms) is taken into account instead of Eckart's non-causal theory. To this purpose, we find numerical solutions for the gravitational potential and compare its behaviour with the corresponding ΛCDM case. Eckart's and the full causal theory seem to be disfavoured, whereas the truncated theory leads to results similar to those of the ΛCDM model for a bulk viscous speed in the interval 10 −11 ≪ c 2 b 10 −8 . Tentatively relating such value to a square propagation velocity of the order of T /m of perturbations in a non-relativistic gas of particles with mass m at the epoch of matter-radiation equality, this may be compatible with a mass range 0.1 GeV m ≪ 100 GeV.

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Stability and causality in dissipative relativistic fluids

Cited by 609 publications

References 7 publications

Causal theory of relativistic dissipative hydrodynamics

Causal theory of relativistic dissipative hydrodynamics

Nonlinear waves in second order conformal hydrodynamics

Bulk viscous cosmology with causal transport theory

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