Generic instabilities in first-order dissipative relativistic fluid theories

Hiscock, William A.; Lindblom, Lee

doi:10.1103/physrevd.31.725

Cited by 631 publications

(778 citation statements)

References 8 publications

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“…Equation (10.42) implies that the theory is stable even for m 2 < 0 if 43) which is known as the Breitenlohner-Freedman bound [3]. The slow falloff behaves as φ ∼ u ∆ − .…”

Section: Massive Scalar Fieldmentioning

confidence: 99%

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AdS/CFT Duality User Guide

Natsuume

2015

Lecture Notes in Physics

180

215

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This is the draft/updated version of a textbook on "real-world" applications of the AdS/CFT duality for beginning graduate students in particle physics and for researchers in the other fields. The aim of this book is to provide background materials such as string theory, general relativity, nuclear physics, nonequilibrium physics, and condensed-matter physics as well as some key applications of the AdS/CFT duality in a single textbook. Contents: (1) Introduction, (2) General relativity and black holes, (3) Black holes and thermodynamics, (4) Strong interaction and gauge theories, (5) The road to AdS/CFT, (6) The AdS spacetime, (7) AdS/CFT - equilibrium, (8) AdS/CFT - adding probes, (9) Basics of nonequilibrium physics, (10) AdS/CFT - nonequilibrium, (11) Other AdS spacetimes, (12) Applications to quark-gluon plasma, (13) Basics of phase transition, (14) AdS/CFT - phase transition, (15) Exercises.Comment: 309 pages. Comments welcome. Published edition is available from Springer (Lecture Notes in Physics 903). Translated from a Japanese book originally published in 2012; v2: various improvements; v3: minor corrections, v4: added materials & minor improvements after publication (see "Preface for the arXiv edition" for details). http://link.springer.com/book/10.1007/978-4-431-55441-

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“…Equation (10.42) implies that the theory is stable even for m 2 < 0 if 43) which is known as the Breitenlohner-Freedman bound [3]. The slow falloff behaves as φ ∼ u ∆ − .…”

Section: Massive Scalar Fieldmentioning

confidence: 99%

“…Unphysical instabilities: Standard relativistic first-oder hydrodynamics has unphysical instabilities [43,44]. Second-order hydrodynamics is free from this problem (at least for linear perturbations).…”

Section: Revisiting Diffusion Problem: Hydrodynamic Applicationmentioning

confidence: 99%

AdS/CFT Duality User Guide

Natsuume

2015

Lecture Notes in Physics

180

215

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“…One can derive a perturbation solution for the heat flux, q µ e , by expanding the entropy current in powers of q µ e and imposing the second law of thermodynamics. The most straightforward relativistic generalisation of the classical, isotropic heat flux first written down by Eckart (1940) is first order in this expansion and was later shown by Hiscock & Lindblom (1985) to be unconditionally unstable, precisely because it violated causality showed the same for anisotropic conduction). Israel & Stewart (1979) derived a second order solution for q µ e which was later shown to be conditionally stable (Hiscock & Lindblom 1985;.…”

Section: Anisotropic Electron Conductionmentioning

confidence: 99%

Electron thermodynamics in GRMHD simulations of low-luminosity black hole accretion

Ressler

Tchekhovskoy

Quataert

et al. 2015

Mon. Not. R. Astron. Soc.

171

238

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Simple assumptions made regarding electron thermodynamics often limit the extent to which general relativistic magnetohydrodynamic (GRMHD) simulations can be applied to observations of low-luminosity accreting black holes. We present, implement, and test a model that self-consistently evolves an entropy equation for the electrons and takes into account the effects of spatially varying electron heating and relativistic anisotropic thermal conduction along magnetic field lines. We neglect the back-reaction of electron pressure on the dynamics of the accretion flow. Our model is appropriate for systems accreting at ≪ 10 −5 of the Eddington accretion rate, so radiative cooling by electrons can be neglected. It can be extended to higher accretion rates in the future by including electron cooling and proton-electron Coulomb collisions. We present a suite of tests showing that our method recovers the correct solution for electron heating under a range of circumstances, including strong shocks and driven turbulence. Our initial applications to axisymmetric simulations of accreting black holes show that (1) physically-motivated electron heating rates that depend on the local magnetic field strength yield electron temperature distributions significantly different from the constant electron to proton temperature ratios assumed in previous work, with higher electron temperatures concentrated in the coronal region between the disc and the jet; (2) electron thermal conduction significantly modifies the electron temperature in the inner regions of black hole accretion flows if the effective electron mean free path is larger than the local scale-height of the disc (at least for the initial conditions and magnetic field configurations we study). The methods developed in this work are important for producing more realistic predictions for the emission from accreting black holes such as Sagittarius A* and M87; these applications will be explored in future work.

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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 Remarksmentioning

confidence: 73%

“…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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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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Generic instabilities in first-order dissipative relativistic fluid theories

Cited by 631 publications

References 8 publications

AdS/CFT Duality User Guide

AdS/CFT Duality User Guide

Electron thermodynamics in GRMHD simulations of low-luminosity black hole accretion

Causal theory of relativistic dissipative hydrodynamics

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