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Full Description
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.
Contents
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.- 1.3 Interaction of Gravitational and Electromagnetic Waves.- 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.- 2.3 Stationary Gravitational Fields.- 2.4 Energetics 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.- 4.2 Asymptotic Theory of Scattering of Wave Packets in the Gravitational Field of a Black Hole.- 4.3 Wave Fields Outside a Collapsing Star.- 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.- 5.4 Relativistic Magnetohydrodynamics.- 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.- 6. SomeProblems of the Dynamics of Waves in Relativistic Cosmology.- 6.1 Development of Inhomogeneities in Models of the Universe with a Cosmological Magnetic Field.- 6.2 Self-Similar Motions of a Photon Gas in the Friedman-Lemaître Model.- 7. Acoustic Phenomena in Strong Gravitational and Magnetic Fields.- 7.1 Propagation of Nonlinear Short Acoustic Waves.- 7.2 The Form of the Magnetosphere in a Nonuniform Plasma.- 7.3 Generation of Acoustic Waves by the Rotating Magnetosphere in the Stellar Wind.- 7.4 The Stability of Uniform Nonlinear Pulsations of Gravitating Gaseous Spheres.- 7.5 Nonlinear Transverse Oscillations at Resonance in a Layer of an Ideally Conducting Fluid in a Magnetic Field.- 7.6 Excitation of Shock Waves in a Layer of an Ideally Conducting Gas at Resonance in a Magnetic Field.- References.
