Relativistic Boltzmann theory in D + 1 spacetime dimensions

Boisseau, B.; Leeuwen, W.A. van

doi:10.1016/0003-4916(89)90249-2

Cited by 24 publications

(40 citation statements)

References 16 publications

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“…The relation (74) can be proven by straightforward calculations by using the properties of Bessel's function (67) (see a similar proof for isotropic spacetimes in [3]). …”

Section: Enthalpy Specific Heats and Entropymentioning

confidence: 92%

“…By definition (like in usual the relativistic Boltzmann theory [7,15,3]) the cross section σ is the division of the number (48) to the number (51)…”

Section: The Cross Section In La-spacetimementioning

confidence: 99%

“…In consequence, it was proved (see [8] and [3]) that the scalar parts of A (p) and B (p) are determined respectively up to functions of the forms ϕ = a + b α p α and b α p α . We emphasize that solutions of the transport equations (84) (see next subsections) will be expressed in terms of A, B, and C.…”

Section: On the Solution Of Locally Anisotropic Transport Equationsmentioning

confidence: 99%

“…with the transport coefficients (the heat conductivity λ, the shear viscosity η, and the volume viscosity coefficient η (v) ; in order to compare with formulas from [3] we shall introduce explicitly the light velocity constant c) defined as…”

Section: Linear Laws For Locally Anisotropic Non-equilibrium Thermodymentioning

confidence: 99%

“…On both type of locally isotropic and anisotropic spacetimes one holds the socalled conditions of fit (see, for instance, [3])…”

Section: Linear Laws For Locally Anisotropic Non-equilibrium Thermodymentioning

confidence: 99%

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Locally Anisotropic Kinetic Processes and Thermodynamics in Curved Spaces

Vacaru

2001

Annals of Physics

141

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The kinetic theory is formulated with respect to anholonomic frames of reference on curved spacetimes. By using the concept of nonlinear connection we develop an approach to modelling locally anisotropic kinetic processes and, in corresponding limits, the relativistic non-equilibrium thermodynamics with local anisotropy. This lead to a unified formulation of the kinetic equations on (pseudo) Riemannian spaces and in various higher dimensional models of Kaluza-Klein type and/or generalized Lagrange and Finsler spaces. The transition rate considered for the locally anisotropic transport equations is related to the differential cross section and spacetime parameters of anisotropy. The equations of states for pressure and energy in locally anisotropic thermodynamics are derived. The obtained general expressions for heat conductivity, shear and volume viscosity coefficients are applied to determine the transport coefficients of cosmic fluids in spacetimes with generic local anisotropy. We emphasize that such locally anisotropic structures are induced also in general relativity if we are modelling physical processes with respect to frames with mixed sets of holonomic and anholonomic basis vectors which naturally admits an associated nonlinear connection structure.gr-qc/0001060; accepted to Annals of Physics (NY)

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“…The relation (74) can be proven by straightforward calculations by using the properties of Bessel's function (67) (see a similar proof for isotropic spacetimes in [3]). …”

Section: Enthalpy Specific Heats and Entropymentioning

confidence: 92%

“…By definition (like in usual the relativistic Boltzmann theory [7,15,3]) the cross section σ is the division of the number (48) to the number (51)…”

Section: The Cross Section In La-spacetimementioning

confidence: 99%

Section: On the Solution Of Locally Anisotropic Transport Equationsmentioning

confidence: 99%

Section: Linear Laws For Locally Anisotropic Non-equilibrium Thermodymentioning

confidence: 99%

“…On both type of locally isotropic and anisotropic spacetimes one holds the socalled conditions of fit (see, for instance, [3])…”

Section: Linear Laws For Locally Anisotropic Non-equilibrium Thermodymentioning

confidence: 99%

See 3 more Smart Citations

Locally Anisotropic Kinetic Processes and Thermodynamics in Curved Spaces

Vacaru

2001

Annals of Physics

141

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Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials

Strain

2010

Commun. Math. Phys.

114

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In this paper it is shown that unique solutions to the relativistic Boltzmann equation exist for all time and decay with any polynomial rate towards their steady state relativistic Maxwellian provided that the initial data starts out sufficiently close in L ∞ ℓ . If the initial data are continuous then so is the corresponding solution. We work in the case of a spatially periodic box. Conditions on the collision kernel are generic in the sense of [18]; this resolves the open question of global existence for the soft potentials.

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