The Relativistic Boltzmann Equation: Theory and Applications

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.- 9.2Propagation 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.