This book is an updated and modified translation of the Russian edition of 1984. In the present edition, certain sections have been abridged (in particular, Sects. 6.1 and 8.3) and the bibliography has been expanded. There are more detailed discus­ sions of the group properties of integrable systems of equations of mathematical physics (Sect. 3.4) and of the Riemannian problem in the context of the infinite­ dimensional internal symmetry groups of these systems of equations. There is an extended discussion of the reasons for the acceleration and retardation of pulsars in connection with more recent achievements of X-ray astronomy. Part of the material of Chap. 8 of the Russian edition has been included in Chap. 7; thus the number of chapters has been reduced to seven. S. Chandrasekhar set for me an example of brilliant analytical penetration into the essence of physical problems, and my book touches on his work in many in­ stances. The results of modem quantum theories of strong fields are not presented, but they can be found in the fundamental monographs Quantwn Electrodynamics of Strong Fields by W. Greiner, B. Muller, J. Rafelski (Sprioger-Verlag, Berlin, Heidelberg, New York 1985) and Quantwn Effects in Intense External Fields [in Russian] by A. Grib, S. Mamaev, W. Mostepanenko (Energoatomizdat, Moscow 1988). This book was translated by Dr. N. M. Queen; I am very grateful to him. I thank sincerely H. Latta, C.-D. Bachem, V. Rehman, S. von Kalckreuth for preparing of the english manuscript.

Inhalt

1. Gravitational Waves in Strong Gravitational Fields.- 1.1 Formalism of Complex Null Tetrads and Petrov Classification of Algebraic Types of the Weyl Tensor.- 1.2 Gravitational Waves and Generalized Solutions of the Equations of the Electrovacuum.- 1.2.1 Properties of Families of Isotropic Geodesics in General Relativity.- 1.2.2 Propagation of Breaks in the Gravitational Field and Their Algebraic Classification.- 1.2.3 Decay of an Arbitrary Break in the Vacuum Gravitational Field.- 1.2.4 The Interaction of Short Gravitational and Electromagnetic Waves in Arbitrary External Electromagnetic Fields.- 1.2.5 Algebraic Structure of Perturbations of the Weyl Tensor in the Case of High-Frequency Waves.- 1.2.6 Behavior of Short-Wave Perturbations of the Gravitational Field Near Caustic Surfaces.- 1.3 Interaction of Gravitational and Electromagnetic Waves.- 1.3.1 Curvature of Space-Time in a Plane Electromagnetic Wave.- 1.3.2 Nonlinear Interaction of Plane Waves.- 1.3.3 Propagation of Weak Electromagnetic and Gravitational Waves in the Field of a Strong Electromagnetic Wave.- 1.3.4 Oscillatory Character of Solutions Near a Singularity.- 1.4 Conditions on Surfaces with Strong Breaks in Theories of the Gravitational Field.- 2. The Classical Theory of Black Holes.- 2.1 Asymptotically Flat Gravitational Fields.- 2.2 Basic Elements of the Theory of Lie Groups and Exterior Forms.- 2.2.1 The Concept of Lie Groups.- 2.2.2 The Concept of Skew and Differential Forms.- 2.2.3 Frobenius's Theorem.- 2.3 Stationary Gravitational Fields.- 2.4 Energetics of Black Holes.- 2.4.1 Temperature of a Black Hole.- 2.4.2 Electrostatic Potential of a Black Hole.- 2.4.3 Formula for the Mass of a Black Hole.- 2.4.4 "Thermodynamics" of Black Holes.- 3. Stationary Axially Symmetric Fields in General Relativity.- 3.1 Canonical Equations of Massless Fields Admitting Abelian Two-Parameter Groups of Motions.- 3.2 Infinite-Dimensional Algebra and Lie Group of the Equations for the Neutrino Electrovacuum.- 3.3 General Solution of the Einstein-Maxwell Equations for Ernst Data Regular Locally on the Symmetry Axis.- 3.4 Lie-Bäcklund Groups of Integrable Systems of Mathematical Physics.- 4. Propagation of Waves in the Gravitational Fields of Black Holes.- 4.1 Propagation of Short Waves in the Field of a Charged Black Hole.- 4.1.1 Short Waves in the Nordström-Reissner Field.- 4.1.2 Short Waves in the Neighborhood of a Rotating Charged Black Hole.- 4.2 Asymptotic Theory of Scattering of Wave Packets in the Gravitational Field of a Black Hole.- 4.3 Wave Fields Outside a Collapsing Star.- 4.3.1 Derivation of the Basis Equations.- 4.3.2 Boundary Conditions and General Properties of the Reflection and Transmission Coefficients of Waves.- 4.3.3 Properties of Radiation Emitted by a Collapsing Body Near the Horizon.- 4.3.4 Behavior of the Transmission Coefficient for Small w.- 4.3.5 Laws of Attenuation of the "Tails" of the Multipole Radiation.- 5. Relativistic Hydrodynamics.- 5.1 Relativistic Dynamics of a Point and Gas of Free Particles.- 5.2 Thermodynamic Equilibrium in an Ideal Gas.- 5.3 Relativistic Dynamics and Acoustics of an Ideal Gas.- 5.3.1 Shock Waves and Vortex Motions of an Ideal Gas.- 5.3.2 Potential Motions.- 5.3.3 Acoustic Waves in a Relativistic Gas.- 5.3.4 Nonlinear Acoustics of an Expanding Universe: Relativistic Theory.- 5.4 Relativistic Magnetohydrodynamics.- 5.4.1 Shock Waves in Magnetohydrodynamics and the Hugoniot Adiabat.- 5.4.2 Properties of MHD Breaks.- 5.4.3 Relative Positions of the Poisson and Hugoniot Adiabats.- 5.5 Hydrodynamical Flow Resulting from Production of Ultrarelativistic Particles in the Field of a Black Hole.- 5.6 Self-Similar Motions of an Ultrarelativistic Gas with Spherical or Cylindrical Symmetry.- 5.6.1 Qualitative Investigation of (5.6.5).- 5.6.2 Ejection of Matter from a Singular Point (Axis) at the Instant t = 0.- 5.6.3 Solution of the Cauchy Problem.- 6. Some Problems of the Dynamics of Waves in Relativistic Cosmology.- 6.1 Development of Inhomogeneities in Models of the Universe with a Cosmological Magnetic Field.- 6.1.1 Unperturbed Solution.- 6.1.2 Notation for Small Perturbations and Coordinate Restrictions.- 6.1.3 Equations of Conservation of Energy-Momentum and of the Magnetic Induction.- 6.1.4 A Closed System for the Odd Perturbations.- 6.1.5 A Closed System for the Even Perturbations.- 6.1.6 Exact Solutions of the Linearized Equations Corresponding to Perturbations of the Coordinate System.- 6.1.7 Closed System of Equations for the Even Perturbations.- 6.1.8 Analysis of the Closed System of Equations for Odd Perturbations.- 6.1.9 Analysis of the Closed System for Even Short-Wave Perturbations.- 6.1.10 Evolution of Perturbations of Arbitrary Finite Scales Near a "Pancake" Singularity.- 6.2 Self-Similar Motions of a Photon Gas in the Friedman-Lemaître Model.- 6.2.1 Derivation of a Closed System of Ordinary Differential Equations and Conditions on Shock Waves.- 6.2.2 Friedman Solution and Qualitative Investigation of the System of Equations for x(?) and V(?).- 6.2.3 Discussion of the Results.- 7. Acoustic Phenomena in Strong Gravitational and Magnetic Fields.- 7.1 Propagation of Nonlinear Short Acoustic Waves.- 7.1.1 Derivation of the Model Equations.- 7.1.2 The Energy Density, Enthalpy Flux Vector, and Momentum Density in an Acoustic Wave Traveling Through an Arbitrary Background.- 7.1.3 Distortion of Short Acoustic Waves.- 7.1.4 Reflection of Acoustic Waves from Strong Breaks.- 7.2 The Form of the Magnetosphere in a Nonuniform Plasma.- 7.2.1 The Form of the Static Magnetosphere in a Nonuniform Plasma.- 7.2.2 Shape of the Magnetosphere of a Star Rotating in the Supersonic Regime.- 7.3 Generation of Acoustic Waves by the Rotating Magnetosphere in the Stellar Wind.- 7.3.1 Acoustic Waves in an Isothermal Atmosphere.- 7.3.2 Generation of Short Waves.- 7.3.3 Inversion of Acoustic Waves.- 7.3.4 Heating of the Plasma Due to Dissipation of Acoustic Waves.- 7.3.5 Inclusion of Viscosity of the Gas in Calculating the Torque Acting on the Rotating Magnetosphere.- 7.3.6 Supersonic Rotation of a Pulsar.- 7.3.7 A Model Problem of Stationary Accretion of a Gas with Index of the Adiabat ?