Relativistic Boltzmann Equation

Cercignani, Carlo; Kremer, Gilberto M.

doi:10.1007/978-3-0348-8165-4_2

Cited by 100 publications

(166 citation statements)

References 14 publications

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“…II. In the presence of the external field that is not directly related with the momentum, the RBT equation can be written in RTA as follows [100,101],…”

Section: Electrical Conductivitymentioning

confidence: 99%

Shear viscosity η to electrical conductivity σel ratio for an anisotropic QGP

et al. 2017

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We study the transport properties of strongly interacting matter in the context of ultrarelativistic heavy ion collision experiments. We calculate the transport coefficients viz. shear viscosity (η) and electrical conductivity (σ el ) of the quark gluon plasma phase in the presence of momentum anisotropy arising from different expansion rates of the medium in longitudinal and transverse direction. We solve the relativistic Boltzmann kinetic equation in relaxation time approximation to calculate the shear viscosity and electrical conductivity. The calculation are performed within the quasiparticle model to estimate these transport coefficients and discuss the connection between them. We also compare the electrical conductivity results calculated from the quasiparticle model with the ideal case. We compare our results with the corresponding results obtained in different lattice as well as model calculations.

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“…II. In the presence of the external field that is not directly related with the momentum, the RBT equation can be written in RTA as follows [100,101],…”

Section: Electrical Conductivitymentioning

confidence: 99%

Shear viscosity η to electrical conductivity σel ratio for an anisotropic QGP

et al. 2017

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“…For z > y, the first term diverges in the limit r → r h , so we can drop 1 and have h ∝ (r→r h ) √ 1 − v 2 /u yielding the third line in (31). Using the law of motion [20,37] …”

Section: A Flow In the Vicinity Of The Horizonsmentioning

confidence: 99%

“…The statistics of non-degenerate and degenerate gases result in different one-particle distribution functions [20,30,31]. Non-degenerate gases obey Maxwell-Boltzmann statistics and degenerate gases obey either Fermi-Dirac statistics, if they have half-integral spin, or Bose-Einstein statistics, if they have integral spin.…”

Section: Applications: Non-degenerate and Degenerate Gasesmentioning

confidence: 99%

“…The momentum particle density 4 dN/dp 1 dp 2 dp 3 ∝ p −3 F , with ∑ 3 i=1 (p i ) 2 = | p| and N being the fermions number, assumes an arbitrarily large value in the vicinity of the horizons. Here again we give only the limiting expressions of (n, p, ǫ) for the Bose-Einstein fluids (see, for instance, [20,30,31,34] for more details).…”

Section: Non-relativistic Limit: P F ≪ MCmentioning

confidence: 99%

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Accretion of rotating fluids onto stationary solutions

Azreg‐Aïnou

2017

Phys. Rev. D

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We consider a general stationary solution and derive the general laws for accretion of rotating perfect fluids. For non-degenerate and degenerate Fermi and Bose fluids we derive new effects that mimic the center-of-mass-energy effect of two colliding particle in the vicinity of horizons. Nondegenerate fluids see their chemical potential grow arbitrarily and ultra-relativistic Fermi fluids see their specific enthalpy and Fermi momentum grow arbitrarily too while the latter vanishes gradually for non-relativistic Fermi fluids. For degenerate Bose fluids two scenarios remain possible as the fluid approaches a horizon: a) The Bose-Einstein condensation ceases or b) the temperature drops gradually down to zero. The critical flow is also investigated. I. WHAT IS ACCRETION?Given a metric solution of spacetime, a geodesic motion is the process by which a massive or massless test particle "falls" freely. The fall motion may be bounded (circular motion or else) or unbounded (scattering motion). The free fall of the test particle does not disturb, affect, or modify the given geometry: No back reaction effects are taken into consideration. Moreover, no group motion is treated in geodesic motion. Back reaction effects are present in the calculation of gravitational self forces where the motion of the "small" body is still seen as geodesic in the perturbed metric.Accretion is an advanced state of motion. It describes group motion with and without back reaction and it is generally non-geodesic. By group motion it is meant that the accreting matter is modeled by a fluid and that each fluid element encompasses a) a sufficiently large number of particles to be described statistically by an average pressure, average temperature, average particle number density, and average energy density; b) a sufficiently small number of particles compared to the whole system (accreting matter, atmosphere, etc). These conditions are easily met in astrophysics and atmospheric motion. The presence of a gradient of pressure, which is a sort of fluid group self force, renders the accretion motion non-geodesic.In accretion motion back reaction effects are taken into consideration in numerical and simulation analyses [1][2][3]. Full analytical treatments [4-8] drop back reaction effects for simplicity and cognitive treatments [9-15] may include emission effects and neglect back reaction too.All the above-mentioned treatments make common simplificative physical assumptions of symmetry concerning both the given background geometry and the fluid. They assume the background metric to remain stationary and time-independent during accretion [16]. The analysis remains valid for accretion time, larger than free-fall time, and much smaller than the ratio mass/(mass rate change) of the star.In this work we will keep using the standard set of simplificative assumptions to describe the accretion of rotating perfect fluids onto rotating black holes with no back reaction or emission effects. In Sec. II we present the accretion model and in sec. III we derive the gen...

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“…We start with a short introduction to the problem, see [5] for more details. The speed of light and the rest mass of particles are both normalized to unity, i.e., m = c = 1; the convention on the signature is (+ − −−).…”

Section: The Relativistic Casementioning

confidence: 99%

On blowup for gain‐term‐only classical and relativistic Boltzmann equations

Andréasson

Calogero

Illner

2004

Math Methods in App Sciences

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We show that deletion of the loss part of the collision term in all physically relevant versions of the Boltzmann equation, including the relativistic case, will in general lead to blowup in finite time of a solution and hence prevent global existence. Our result corrects an error in the proof given in Ref. [12], where the result was announced for the classical hard sphere case; here we give a simpler proof which applies much more generally.

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Relativistic Boltzmann Equation

Cited by 100 publications

References 14 publications

Shear viscosity η to electrical conductivity σel ratio for an anisotropic QGP

Shear viscosity η to electrical conductivity σel ratio for an anisotropic QGP

Accretion of rotating fluids onto stationary solutions

On blowup for gain‐term‐only classical and relativistic Boltzmann equations

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