Anmerkung: Intro -- Preface -- References -- Contents -- About the Authors -- 1 Relativistic Fluid Dynamics -- 1.1 Thermodynamics -- 1.2 Relativistic Ideal Fluid Dynamics -- 1.2.1 Conserved Currents in an Ideal Fluid -- 1.2.2 Equations of Motion -- 1.2.3 Covariant Thermodynamics and Entropy Production -- 1.3 Relativistic Dissipative Fluid Dynamics -- 1.3.1 Matching Conditions -- 1.3.2 Tensor Decomposition of τµν -- 1.3.3 Definition of the Local Rest Frame and Equations of Motion -- 1.3.4 Relativistic Navier-Stokes Theory -- 1.3.5 Gradient Expansion and Navier-Stokes Theory -- 1.4 Causal Fluid Dynamics -- 1.4.1 Diffusion Equation and Acausality in Heat Conduction -- 1.4.2 Transient Theory of Fluid Dynamics -- 1.5 Transient Thermodynamics and Israel-Stewart Theory -- 1.6 Non-hydrodynamic Modes and the Origin of the Relaxation Time -- 2 Linear Stability and Causality -- 2.1 Fluid-Dynamical Equations Linearized Around Global Equilibrium -- 2.2 Linearized Fluid-Dynamical Equations in Fourier Space -- 2.2.1 Tensor Decomposition in Fourier Space -- 2.2.2 Longitudinal and Transverse Components -- 2.3 Ideal Fluid Dynamics -- 2.4 Relativistic Navier-Stokes Theory -- 2.4.1 Transverse Modes -- 2.4.2 Longitudinal Modes -- 2.4.3 Causality and Stability of Navier-Stokes Theory -- 2.5 Transient Theory of Fluid Dynamics -- 2.5.1 Transverse Modes in the Rest Frame -- 2.5.2 Longitudinal Modes in the Rest Frame -- 2.5.3 Stability for a Moving Background -- 2.5.4 Causality of Wave Propagation -- 2.6 Summary -- 3 Analytical Solutions and Transient Dynamics -- 3.1 Fluid Dynamics in a General Metric System -- 3.2 Bjorken Flow -- 3.2.1 Coordinates and Kinematic Properties -- 3.2.2 Fluid-Dynamical Equations -- 3.2.3 Ideal-Fluid Limit -- 3.2.4 Relativistic Navier-Stokes Theory -- 3.2.5 Transient Theory of Fluid Dynamics -- 3.2.6 Gradient Expansion of Transient Fluid Dynamics. , 3.3 Gubser Flow -- 3.3.1 Coordinates and Kinematical Properties -- 3.3.2 Fluid-Dynamical Equations of Motion -- 3.3.3 Ideal-Fluid Limit -- 3.3.4 Relativistic Navier-Stokes Theory -- 3.3.5 Transient Theory of Fluid Dynamics -- 3.3.6 Gradient Expansion of Transient Fluid Dynamics -- 3.3.7 Divergence of the Gradient Expansion -- 3.3.8 Domain of Applicability of the Gradient Expansion -- 3.3.9 Slow-Roll Expansion -- 3.3.10 Divergence of the Slow-Roll Series -- 3.3.11 Attractor Solution -- 3.4 Summary -- 4 Microscopic Origin of Transport Coefficients: Linear-Response Theory -- 4.1 Preliminaries -- 4.2 Equivalence Between Gradient Expansion and Taylor Series -- 4.3 The Role of the Analytical Structure of tildeGR(ω) -- 4.3.1 tildeGR(ω) with One Pole -- 4.3.2 tildeGR(ω) with Two Poles -- 4.3.3 tildeGR(Q) with N Poles -- 4.4 Applications -- 4.4.1 The Linearized Boltzmann Equation -- 4.4.2 Linear-Response Theory and Metric Perturbations -- 4.5 Discussion -- 4.6 Summary -- 5 Fluid Dynamics from Kinetic Theory: Traditional Approaches -- 5.1 Matching Fluid-Dynamical with Kinetic Degrees of Freedom -- 5.1.1 Macroscopic Conservation Laws -- 5.1.2 Fluid-Dynamical Variables and Matching Conditions -- 5.2 Chapman-Enskog Theory -- 5.2.1 Solving the Chapman-Enskog Expansion: Zeroth- and First-Order Solutions -- 5.2.2 Minimal Truncation Scheme -- 5.3 Israel-Stewart Theory -- 5.3.1 14-Moment Approximation -- 5.3.2 Matching Procedure -- 5.3.3 Moment Equations -- 5.3.4 Calculation of the Collision Integrals -- 5.3.5 Hydrodynamic Equations of Motion -- 5.4 Summary -- 6 Method of Moments: Equilibrium Reference State -- 6.1 Moment Expansion -- 6.2 Equations of Motion for the Irreducible Moments -- 6.3 Generalized Collision Term -- 6.3.1 Computation of the Linear Collision Term -- 6.3.2 Computation of the Nonlinear Collision Term -- 6.4 Summary. , 6.5 Appendix 1: Irreducible Projection Operators -- 6.6 Appendix 2: Thermodynamic Integrals and Properties -- 6.7 Appendix 3: Orthogonality of the Irreducible Tensors -- 6.8 Appendix 4: Orthogonal Polynomials -- 7 Method of Moments: Convergence Properties -- 7.1 Boltzmann Equation and Fluid-Dynamical Variables -- 7.2 Bjorken Flow -- 7.2.1 Method of Moments -- 7.2.2 Moment Equations -- 7.2.3 Results -- 7.3 Gubser Flow -- 7.3.1 Method of Moments -- 7.4 Summary -- 8 Fluid Dynamics from the Method of Moments -- 8.1 Power Counting -- 8.2 Resummed Transient Relativistic Fluid Dynamics -- 8.3 Resummed Transient Relativistic Fluid Dynamics: 14 Dynamical Variables -- 8.4 Transport Coefficients -- 8.4.1 14-Moment Approximation -- 8.4.2 23-Moment Approximation and Beyond -- 8.5 Discussion: Navier-Stokes Limit and Causality -- 8.6 Resummed Transient Relativistic Fluid Dynamics: 23 Dynamical Variables -- 8.7 Comparisons with Microscopic Theory -- 8.7.1 Stationary Shock Solutions -- 8.8 Summary -- 8.9 Appendix 1: Transport Coefficients in Eq. (8.44) -- 8.10 Appendix 2: Calculation of the Collision Integrals -- 8.10.1 Particle-Diffusion Current -- 8.10.2 Shear-Stress Tensor -- 8.11 Appendix 3: Calculation of γ1(2) -- 8.11.1 14-Moment Approximation -- 8.11.2 23-Moment Approximation -- 8.12 Appendix 4: Transport Coefficients in Sect. 8.6 -- 9 Method of Moments: Anisotropic Reference State -- 9.1 Fluid-Dynamical Variables -- 9.2 Anisotropic State -- 9.3 Expansion Around the Anisotropic Distribution Function -- 9.4 Equations of Motion for the Irreducible Moments -- 9.5 Collision Integrals -- 9.6 Summary -- 9.7 Appendix 1: Irreducible Projection Operators -- 9.8 Appendix 2: Generalized Thermodynamic Integrals -- 9.9 Appendix 3: Generalized Thermodynamic Integrals in the Equilibrium Limit -- 9.10 Appendix 4: Orthogonality of the Irreducible Tensors. , 9.11 Appendix 5: Orthogonal Polynomials.

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