Download E-books Magnetohydrodynamics: Waves and Shock Waves in Curved Space-Time (Mathematical Physics Studies) PDF

For seventy years, we've got recognized that Einstein's idea is largely a idea of propagation of waves for the gravitational box. Confusion enters, besides the fact that, in the course of the proven fact that the note wave, in physics, implies occasionally repetition and infrequently no longer. This confusion is frequently elevated by means of he use of Fourier transforms, through which a disturbanse which seems to be with no repetition is resolved into periodic wave-trains with all frequencies. yet, in a basic curved space-time, now we have not anything equivalent to Fourier transforms. right here, we reflect on systematically waves akin to the propagation of discontinuities of actual amounts describing both fields (essentially electromagnetic fields and gravitational field), or the movement of a fluid, or jointly, in magnetohydrodynamics, the adjustments in time of a box and of a fluid. the most equations, for different studied phenomena, represent a hyperbolic approach and the research of a proper Cauchy challenge is feasible. We name usual waves the case within which the spinoff of better order showing within the procedure are discontinuous on the traverse of a hypersurface, the wave entrance ; we name surprise waves the case the place the derivatives of an order inferior via one are discontinuous on the traverse of a wave entrance. XI xii PREFACE From 1950, many famous scientits (Taub, Synge, Choquet-B ruhat, etc.) have studied the corresponding equations for various actual phenomena : structures linked to the electromagnetic and gravitational fields, to hydrodynamics and to magnetohydrodynamics.