Oscillations and Waves

This book emerged from a course given at Moscow State University and provides an introduction to current research in general relativity, relativistic gas dynamics, and cosmology, touching as well on the different methods used in wave theory. Each chapter begins with an elementary introduction and then proceeds to a more sophisticated discussion including a presentation of the current state of the art.

Contenu

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.