Overview

This text is written both as a reference book for researchers in physics, astrophysics and applied mathematics, and as a textbook for graduate and postgraduate students. In particular, the book provides an introduction to special and general relativity theory. The aim of the 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.

Full Product Details

Author:   Carlo Cercignani ,  Gilberto M. Kremer
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   2002 ed.
Volume:   22
Dimensions:   Width: 15.50cm , Height: 2.20cm , Length: 23.50cm
Weight:   1.620kg
ISBN:  

9783764366933

ISBN 10:   3764366931
Pages:   384
Publication Date:   01 February 2002
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

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.

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