Transient relativistic thermodynamics and kinetic theory

Israel, W.; Stewart, John M.

doi:10.1016/0003-4916(79)90130-1

Cited by 1,708 publications

(2,097 citation statements)

References 11 publications

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“…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;. Here we use a first order reduction of that second order model that has been shown to be both stable and self-consistent (Andersson & Lopez-Monsalvo 2011).…”

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.

174

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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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.

174

238

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“…The resulting hydrodynamics is called causal hydrodynamics or second-order hydrodynamics. In particular, the Israel-Stewart theory [37,38,39] is well-known and has been widely studied in the literature.…”

Section: Revisiting Diffusion Problem: Hydrodynamic Applicationmentioning

confidence: 99%

AdS/CFT Duality User Guide

Natsuume

2015

Lecture Notes in Physics

185

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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“…For the RW metric one has θ = 3H = 3H/a. On the other hand, in the MIS theory [24][25][26] the evolution of Π is described by the following transport equation:…”

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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Transient relativistic thermodynamics and kinetic theory

Cited by 1,708 publications

References 11 publications

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

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

AdS/CFT Duality User Guide

Bulk viscous cosmology with causal transport theory

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