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Magnetohydrodynamics: Waves and Shock Waves in Curved Space-Time

  • Book
  • © 1994

Overview

Authors:
  1. André Lichnerowicz

    1. Collège de France, Paris, France

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Part of the book series: Mathematical Physics Studies (MPST, volume 14)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xii
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  2. Tensor-distributions

    • André Lichnerowicz
    Pages 1-17

  3. Maxwell’s Equations and Electromagnetic Waves over a Curved Space-Time

    • André Lichnerowicz
    Pages 18-32

  4. Einstein’s Equations and the Leray Theorem

    • André Lichnerowicz
    Pages 33-59

  5. Gravitational and Electromagnetic Shock Waves

    • André Lichnerowicz
    Pages 60-97

  6. Relativistic Hydrodynamics

    • André Lichnerowicz
    Pages 98-123

  7. The Equations of Magnetohydrodynamics

    • André Lichnerowicz
    Pages 124-158

  8. Magnetohydrodynamic Shock Waves

    • André Lichnerowicz
    Pages 159-173

  9. Hugoniot’s Function and Applications

    • André Lichnerowicz
    Pages 174-210

  10. Back Matter

    Pages 211-279
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Keywords

About this book

For seventy years, we have known that Einstein's theory is essentially a theory of propagation of waves for the gravitational field. Confusion enters, however, through the fact that the word wave, in physics, implies sometimes repetition and sometimes not. This confusion is often increased by he use of Fourier transforms, by which a disturbanse which appears to be without repetition is resolved into periodic wave-trains with all frequencies. But, in a general curved space-time, we have nothing corresponding to Fourier transforms. Here, we consider systematically waves corresponding to the propagation of discontinuities of physical quantities describing either fields (essentially electromagnetic fields and gravitational field), or the motion of a fluid, or together, in magnetohydrodynamics, the changes in time of a field and of a fluid. The main equations, for the different studied phenomena, constitute a hyperbolic system and the study of a formal Cauchy problem is possible. We call ordinary waves the case in which the derivative of superior order appearing in the system are discontinuous at the traverse of a hypersurface, the wave front ; we call shock waves the case where the derivatives of an order inferior by one are discontinuous at the traverse of a wave front. XI xii PREFACE From 1950, many well-known scientits (Taub, Synge, Choquet-B ruhat, etc.) have studied the corresponding equations for different physical phenomena : systems associated to the electromagnetic and gravitational fields, to hydrodynamics and to magnetohydrodynamics.

Authors and Affiliations

  • Collège de France, Paris, France

    André Lichnerowicz

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