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Field name	Details
Dewey Class	530.138
Title	The Relativistic Boltzmann Equation: Theory and Applications ([EBook]) / by Carlo Cercignani, Gilberto Medeiros Kremer.
Author	Cercignani, Carlo
Added Personal Name	Kremer, Gilberto Medeiros
Other name(s)	SpringerLink (Online service)
Publication	Basel : Birkhäuser , 2002.
Physical Details	X, 384 pages : online resource.
Series	Progress in Mathematical Physics ; 22
ISBN	9783034881654
Summary Note	The aim of this book is to present the theory and applications of the relativistic Boltzmann equation in a self-contained manner, even for those readers who have no familiarity with special and general relativity. Though an attempt is made to present the basic concepts in a complete fashion, the style of presentation is chosen to be appealing to readers who want to understand how kinetic theory is used for explicit calculations. The book will be helpful not only as a textbook for an advanced course on relativistic kinetic theory but also as a reference for physicists, astrophysicists and applied mathematicians who are interested in the theory and applications of the relativistic Boltzmann equation.:
Contents note	1 Special Relativity -- 1.1 Introduction -- 1.2 Lorentz transformations -- 1.3 Tensors in Minkowski spaces -- 1.4 Relativistic mechanics -- 1.5 Electrodynamics in free space -- 2 Relativistic Boltzmann Equation -- 2.1 Single non-degenerate gas -- 2.2 Single degenerate gas -- 2.3 General equation of transfer -- 2.4 Summational invariants -- 2.5 Macroscopic description -- 2.6 Local Lorentz rest frame -- 2.7 Equilibrium distribution function -- 2.8 Trend to equilibrium. H-theorem -- 2.9 The projector ??? -- 2.10 Equilibrium states -- 3 Fields in Equilibrium -- 3.1 The general case -- 3.2 Non-degenerate gas -- 3.3 Degenerate relativistic Fermi gas -- 3.4 Degenerate relativistic Bose gas -- 4 Thermomechanics of Relativistic Fluids -- 4.1 Introduction -- 4.2 Thermodynamics of perfect fluids -- 4.3 Eckart decomposition -- 4.4 Landau and Lifshitz decomposition -- 4.5 Thermodynamics of a single fluid -- 5 Chapman—Enskog Method -- 5.1 Introduction -- 5.2 Simplified version -- 5.3 The integrals Il, I2 and I3 -- 5.4 Transport coefficients -- 5.5 Formal version -- 5.6 Appendix -- 6 Method of Moments -- 6.1 Introduction -- 6.2 Grad distribution function -- 6.3 Constitutive equations for Taßry and Paß -- 6.4 Linearized field equations -- 6.5 Five-field theory -- 6.6 Maxwellian particles -- 6.7 Combined method of Chapman—Enskog and Grad -- 7 Chemically Reacting Gas Mixtures -- 7.1 Introduction -- 7.2 Boltzmann and transfer equations -- 7.3 Maxwell—Jüttner distribution function -- 7.4 Thermodynamics of mixtures -- 7.5 Transport coefficients -- 7.6 Onsager reciprocity relations -- 8 Model Equations -- 8.1 Introduction -- 8.2 The characteristic time -- 8.3 Single non-degenerate gas -- 8.4 Single degenerate gas -- 8.5 Relativistic ionized gases -- 8.6 Appendix -- 9 Wave Phenomena in a Relativistic Gas -- 9.1 Introduction -- 9.2 Propagation of discontinuities -- 9.3 Small oscillations -- 9.4 Shock waves -- 10 Tensor Calculus in General Coordinates -- 10.1 Introduction -- 10.2 Tensor components in general coordinates -- 10.3 Affine connection -- 10.4 Covariant differentiation -- 10.5 Spatial metric tensor -- 10.6 Special relativity in general coordinates -- 11 Riemann Spaces and General Relativity -- 11.1 Introduction -- 11.2 Tensors in Riemannian spaces -- 11.3 Curvature tensor -- 11.4 Physical principles of general relativity -- 11.5 Mechanics in gravitational fields -- 11.6 Electrodynamics in gravitational fields -- 11.7 Perfect fluids -- 11.8 Einstein’s field equations -- 11.9 Solution for weak fields -- 11.10 Exact solutions of Einstein’s field equations -- 11.11 Robertson—Walker metric -- 12 Boltzmann Equation in Gravitational Fields -- 12.1 Introduction -- 12.2 Transformation of volume elements -- 12.3 Boltzmann equation -- 12.4 Transfer equation -- 12.5 Equilibrium states -- 12.6 Boltzmann equation in a spherically symmetric gravitational field -- 12.7 Dynamic pressure in a homogeneous and isotropic universe -- 13 The Vlasov Equation and Related Systems -- 13.1 Introduction -- 13.2 The Vlasov—Maxwell system -- 13.3 The Vlasov—Einstein system -- 13.4 Steady Vlasov—Einstein system in case of spherical symmetry -- 13.5 The threshold of black hole formation -- 13.6 Cosmology with the Vlasov—Einstein system -- Physical Constants -- Modified Bessel Function.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-0348-8165-4
Links to Related Works	Subject References: Astrophysics . Astrophysics and Astroparticles . Classical and Quantum Gravitation, Relativity Theory . Gravitation . Physics . Theoretical, Mathematical and Computational Physics . Authors: author . Cercignani, Carlo . Kremer, Gilberto Medeiros . Corporate Authors: SpringerLink (Online service) . Series: Progress in Mathematical Physics . Classification: 530.138 . 530.138 (DDC 21) .

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The Relativistic Boltzmann Equation: Theory and Applications

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