Relativistic Kinetic Theory: With Applications in Astrophysics and Cosmology

Description

Relativistic kinetic theory has widespread application in astrophysics and cosmology. The interest has grown in recent years as experimentalists are now able to make reliable measurements on physical systems where relativistic effects are no longer negligible. This ambitious monograph is divided into three parts. It presents the basic ideas and concepts of this theory, equations and methods, including derivation of kinetic equations from the relativistic BBGKY hierarchy and discussion of the relation between kinetic and hydrodynamic levels of description. The second part introduces elements of computational physics with special emphasis on numerical integration of Boltzmann equations and related approaches, as well as multi-component hydrodynamics. The third part presents an overview of applications ranging from covariant theory of plasma response, thermalization of relativistic plasma, comptonization in static and moving media to kinetics of self-gravitating systems, cosmological structure formation and neutrino emission during the gravitational collapse. Contents......Page 5 Acknowledgments......Page 10 Acronyms and Definitions......Page 11 Introduction......Page 14 Part I Theoretical Foundations......Page 20 1.1 Nonrelativistic Kinetic Theory......Page 22 1.2 Special Relativistic Kinetic Theory......Page 23 1.3 General Relativistic Kinetic Theory......Page 24 1.4 One-Particle Distribution Function......Page 25 1.5 Invariance of One-Particle Distribution Function......Page 26 1.6 Macroscopic Quantities......Page 27 2.1 Formulation of Kinetic Equation......Page 29 2.2 Collision Integral for Particle Scattering......Page 31 2.3 Boltzmann Equation in General Relativity......Page 32 2.5 Radiative Transfer......Page 34 2.6 Cross Section......Page 37 2.7 Relaxation Time......Page 38 3.1 Covariant Statistical Averaging......Page 39 3.3 The Role of Averaging in Kinetic Theory......Page 41 4.1 Conservation Laws and Relativistic Hydrodynamics......Page 43 4.2 H-theorem......Page 45 4.3 Equilibrium......Page 46 4.4 Relativistic Maxwellian Distribution......Page 49 4.5 Generalized Continuity Equation......Page 50 5.1 The Hierarchy of Kinetic Equations......Page 53 5.2 The First and Second Approximations in Relativistic Transport Equations......Page 57 5.3 The Vlasov-Maxwell System......Page 58 5.4 The Vlasov-Einstein System......Page 61 6.1 Plasma Frequency......Page 63 6.2 Correlations in Plasma......Page 64 6.3 Coulomb Collisions......Page 65 6.4 Characteristic Distances......Page 66 6.5 Microscopic Scales in Kinetic Theory and Hydrodynamics......Page 68 6.6 Relativistic Degeneracy......Page 69 Part II Numerical Methods......Page 72 7.1 Finite Differences and Computational Grids......Page 74 7.2 Stability and Accuracy of Numerical Schemes......Page 76 7.3 Numerical Methods for Partial Differential Equations......Page 79 7.5 ODE Systems and Methods of Their Solution......Page 96 7.6 Stiff Systems and Gear’s Method......Page 98 7.7 Numerical Methods for Linear Algebra......Page 102 8.1 Finite Differences and the Method of Lines......Page 108 8.2 Monte Carlo Method......Page 112 9 Multidimensional Hydrodynamics......Page 119 9.1 High-Order Godunov Methods......Page 120 9.2 Multidimensional Multitemperature High-Order Godunov Code......Page 122 9.3 Riemann Problem Solver in Special Relativity......Page 136 9.4 Particle-Based Methods......Page 139 Part III Applications......Page 146 10 Wave Dispersion in Relativistic Plasma......Page 148 10.1 Collisionless Plasma......Page 150 10.2 Response in an Isotropic Case......Page 151 10.3 Dispersion in Relativistic Thermal Plasma......Page 152 10.4 Landau Damping......Page 154 10.5 Plasma Instabilities......Page 156 10.6 Weibel Instability......Page 157 10.7 Two-Stream Instability......Page 160 10.8 Collisionless Shock Waves......Page 161 11.1 Pair Plasma in Astrophysics and Cosmology......Page 164 11.2 Qualitative Description of the Pair Plasma......Page 166 11.3 Collision Integrals......Page 167 11.4 Relativistic Boltzmann Equation on the Grid......Page 179 11.5 Thermalization Process......Page 180 11.6 Thermalization Timescales......Page 186 11.7 Dynamics and Emission of Mildly Relativistic Plasma......Page 190 11.8 Kinetic Equilibrium and Chemical Potential of Photons......Page 194 12 Kinetics of Particles in Strong Fields......Page 195 12.1 Avalanches in Strong Crossing Laser Fields......Page 196 12.2 Creation and Thermalization of Pairs in Strong Electric Fields......Page 199 12.3 Emission from Hot Bare Quark Stars......Page 211 13.1 The Boltzmann Equation for Compton Scattering......Page 216 13.2 Mean Number of Scatterings......Page 217 13.3 Kompaneets Equation......Page 219 13.4 Sunyaev-Zeldovich Effect......Page 223 13.5 Comptonization in Static Media......Page 227 13.6 Comptonization in Relativistic Outflows......Page 229 13.7 Monte Carlo Simulations of the Photospheric Emission from Relativistic Outflows......Page 233 14 Self-Gravitating Systems......Page 239 14.1 Kinetic Theory of Self-Gravitating Systems......Page 241 14.2 Gravitational Instability......Page 249 14.3 Collisionless (Violent) Relaxation......Page 263 14.4 Quasi-stationary States......Page 266 14.5 Self-Gravitating Systems in Equilibrium......Page 268 14.6 Cosmic Structure Formation......Page 273 15.1 Supernova Models and Neutrinos......Page 275 15.2 Spherically Symmetric Collapse of a Stellar Iron Core with Neutrino Transport......Page 278 15.3 Supernova Explosion Mechanism with Large-Scale Convection and Neutrino Transport......Page 287 Appendix A Hydrodynamic Equations in Orthogonal Curvilinear Coordinates......Page 291 B.1 Collision Integrals for Binary Interactions......Page 294 B.2 Collision Integrals for Binary Reactions with Protons......Page 300 B.3 Collision Integrals for Triple Interactions......Page 302 B.4 Mass Scaling for the Proton-Electron/Positron Reaction......Page 304 C.1 Scattering of Neutrinos on Electrons......Page 306 C.2 Absorption of Neutrinos by Neutrons......Page 308 C.3 Creation of Neutrinos......Page 310 Bibliography......Page 312 Index......Page 339