**Preface**

**1 Hydrodynamics**

1.1 The Mass Conservation Equation

1.2 The Momentum Conservation Equation

1.3 The Energy Conservation Equation

1.4 Bernoulli’s Theorem

1.5 The Equations of Hydrodynamics in Conservative Form

1.6 Viscous Fluids

1.7 Small Perturbations

1.8 Discontinuity

1.8.1 Surfaces of Discontinuity

1.8.2 ShockWaves

1.8.3 Physical Interpretation of Shock Waves

1.8.4 Collisional and Noncollisional Shocks

1.8.5 Formation of a Shock

1.9 Self-similar Solutions

1.9.1 Self-similar Solutions of the Second Kind

1.10 Relativistic Hydrodynamics

1.10.1 Shock Waves in Relativistic Hydrodynamics

1.10.2 The Strong Explosion

1.11 The De Laval Nozzle

1.12 Problems

**2 Magnetohydrodynamics and Magnetic****Fields**

2.1 Equations of Motion

2.1.1 The Limit of Ideal Magnetohydrodynamics

2.1.2 Equations of Motion in a Conservative Form

2.2 The Force Exerted by the Magnetic Field

2.3 Magnetic Flux Freezing

2.4 Small Perturbations in a Homogeneous Medium

2.5 Stability of Tangential Discontinuities

2.6 Two-Temperature Fluids

2.7 Magnetic Buoyancy and Reconnection

2.7.1 Magnetic Buoyancy

2.7.2 Reconnection

2.8 Shock Wave

2.9 Magnetic Fields in Astrophysics

2.9.1 Observations

2.9.2 Origin of Magnetic Fields

2.10 Problems

**3 Radiative Processes**

3.1 Radiative Transport

3.1.1 Radiation Transport

3.2 Low-Temperature Thermal Emission

3.3 Bremsstrahlung

3.4 Synchrotron

3.4.1 Power Radiated by a Single Particle

3.4.2 The Spectrum of a Single Particle

3.4.3 The Spectrum of a Group of Nonthermal Particles

3.4.4 Quantum Corrections

3.4.5 Self-absorption

3.4.6 Cyclotron Lines

3.4.7 Processes in an Intense Magnetic Field

3.4.8 The Razin-Tsytovich Effect

3.5 Compton Processes

3.5.1 Physical Mechanism of the Inverse Compton

3.5.2 The Spectrum of Inverse Compton Processes

3.5.3 About the Compton Parameter

3.5.4 Self-synchro-Compton and Compton Limit

3.5.5 Compton Broadening

3.6 Relativistic Effects

3.6.1 Superluminal Motions

3.6.2 Emission Properties of Relativistic Sources

3.7 Pair Creation and Annihilation

3.8 Cosmological Attenuations

3.8.1 Protons

3.8.2 Photons

3.9 Problems

**4 Nonthermal Particles**

4.1 The Classic Theory of Acceleration

4.1.1 Acceleration

4.1.2 Injection

4.2 Constraints on the Maximum Energy

4.3 More Details in the Newtonian Limit

4.3.1 From the Vlasov Equation to the Convection-Scattering Equation

4.3.2 Scattering in the Angle of Motion in a Mediumat Rest

4.3.3 Scattering and Convection in a Mediumin Motion

4.4 General Discussion

4.4.1 An Equation for *f*

4.4.2 The Small Pitch Angle Scattering Limit

4.4.3 Distributions of Probability *P*u and *P*d

4.4.4 The Particles’ Spectrum

4.4.5 The Equations for *P*u and *P*d

4.4.6 Results

4.5 The Unipolar Inductor

4.6 Problems

**5 Spherical Flows: Accretion and Explosion**

5.1 Accretion from Cold Matter

5.2 Accretion from Hot Matter

5.2.1 The Critical Point

5.3 The Intermediate Case

5.4 Doubts about the Bondi Accretion Rate

5.5 The Eddington Luminosity

5.6 The Efficiency of Spherical Accretion

5.7 Explosive Motions

5.7.1 Supernovae

5.7.2 Gamma Ray Bursts

5.8 Problems

**6 Disk Accretion I**

6.1 Qualitative Introduction

6.2 Fundamental Equations

6.3 Special Relations

6.4 The *α* Prescription

6.5 Equations for the Structure of Disks

6.6 The Standard Solution

6.7 The Origin of Torque

6.8 Disk Stability

6.8.1 Time Scales

6.8.2 Instability

6.9 Lense-Thirring Precession

6.10 Problems

**7 Disk Accretion II**

7.1 Other Disk Models

7.1.1 The Origin of Particles

7.1.2 Dynamic Peculiarities of Pair Plasmas

7.1.3 The Pair Plasma without Input of External Photons

7.1.4 The Pair Plasma with Input of External Photons

7.2 Thick Accretion Disks

7.2.1 Some General Properties

7.2.2 The Inapplicability of the Eddington Limit

7.2.3 Polytropic Models

7.2.4 Properties of Thick Disks

7.3 Nondissipative Accretion Flows

7.4 Further Developments of the Theory

7.4.1 General-Relativistic Corrections

7.4.2 The Fate of Angular Momentum at Large Radii

7.5 Accretion Disks on Magnetized Objects

7.5.1 The Alfv´en Radius

7.5.2 Interaction between the Disk and the Magnetosphere

7.5.3 Accretion Columns

7.6 Boundary Layers

7.7 Problems

**8 Electrodynamics of Compact Objects 419**

8.1 The Gold-PaciniMechanism

8.2 The Magnetospheres Surrounding Pulsars

8.2.1 Quasi-Neutral or Charge-Separated Plasma?

8.2.2 The Goldreich and Julian Magnetosphere

8.2.3 The Pulsar Equation

8.2.4 The Solution

8.2.5 The Transport of Angular Momentum

8.2.6 Discussion

8.3 The Blandford-Znajek Model

8.3.1 The Magnetic Field of a Black Hole

8.3.2 The Black Hole Equation

8.3.3 The Transport of Energy and of Angular Momentum

8.3.4 A Qualitative Discussion

8.3.5 A Simplified Discussion of Total Energetics

8.4 The Generation of Charges

8.5 Disk-Jet Coupling

8.5.1 The Lovelace-Blandford Model

8.5.2 A Special Solution

8.5.3 Discussion

8.5.4 A Model Including Inertial Effects

8.5.5 A Special Solution

8.5.6 Results

8.5.7 A Brief Summary

8.6 Problems

**Appendix**

**A Propagation of Electromagnetic Waves**

**B Orbits Around Black Holes**

B.1 Problem

**C Useful Formulae**

C.1 Vector Identities

C.2 Cylindrical Coordinates

C.3 Spherical Coordinates