Relativistic Fluids and Magneto-fluids: With Applications in Astrophysics and Plasma Physics

348 Pages·2005·5.98 MB·English

by  A. M. Anile

CAMBRIDGE MONOGRAPHS ON
MATHEMATICAL PHYSICS
General editors: P. V. Landshoff, D. R. Nelson, D. W. Sciama, S. Weinberg
RELATIVISTIC FLUIDS AND MAGNETO-FLUIDS
With Applications in Astrophysics and Plasma Physics

RELATIVISTIC FLUIDS AND
MAGNETO-FLUIDS
With Applications in Astrophysics and Plasma Physics
A. M. ANILE
University of Catania
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© Cambridge University Press 1989
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the written permission of Cambridge University Press.
First published 1989
This digitally printed first paperback version 2005
A catalogue record for this publication is available from the British Library
Library of Congress Cataloguing in Publication data
Anile, Angelo Marcello.
Relativistic fluids and magneto-fluids: with applications in
astrophysics and plasma physics /A. M. Anile.
p. cm. - (Cambridge monographs on mathematical physics)
Bibliography: p.
Includes index.
ISBN 0-521-30406-7
1. Plasma astrophysics. 2. Relativistic fluid dynamics.
3. Magnetohydrodynamics. I. Title. II. Series.
QB462.7.A55 1989
523.01-dcl9 88-36742
CIP
ISBN-13 978-0-521-30406-1 hardback
ISBN-10 0-521-30406-7 hardback
ISBN-13 978-0-521-01812-8 paperback
ISBN-10 0-521-01812-9 paperback
TO MY PARENTS
La filosofia e' scritta in questo grandissimo libro che continuamente ci
sta aperto innanzi agli occhi (io dico l'universo), ma non si puo'
intendere se prima non s'impara a intender la lingua, e conoscer i
caratteri, ne' quali e' scritto. Egli e' scritto in lingua matematica, e i
caratteri sono triangoli, cerchi, ed altre figure geometriche, senza i quali
mezzi e' impossibile a intenderne umanamente parola; senza questi e'
un aggirarsi vanamente per un oscuro labirinto.
G. GALILEI, II Saggiatore, Opere, Ed. Nazionale, vol. VI, p. 300.
Certo, volendo, uno puo' anche mettersi in testa di trovare un ordine
nelle stelle, nelle galassie, un ordine nelle finestre illuminate dei
grattacieli vuoti dove il personale della pulizia tra le nove e mezzanotte
da' la cera agli uffici. Giustificare, il gran lavoro e' questo, giustificate se
non volete che tutto si sfasci.
i. CALVINO, Ti con zero, 2nd edition, 1967, G. Einaudi, Torino.
Contents
Preface page xi
1 Introduction 1
2 Mathematical structure 4
2.0 Introduction 4
2.1 Quasi-linear hyperbolic systems in conservation form 5
2.2 The equations of relativistic nondissipative fluid dynamics 9
2.3 Test relativistic fluid dynamics as a quasi-linear hyperbolic
system 17
2.4 Test relativistic magneto-fluid dynamics as a quasi-linear
hyperbolic system 23
2.5 Supplementary conservation laws and symmetrization 43
2.6 Main field for relativistic fluid dynamics 46
2.7 Main field for relativistic magneto-fluid dynamics 52
3 Singular hypersurfaces in space-time 57
3.0 Introduction 57
3.1 Regularly discontinuous tensor fields across a hypersurface 59
4 Propagation of weak discontinuities 71
4.0 Introduction 71
4.1 Characteristic hypersurfaces 73
4.2 Weak discontinuities 80
4.3 Weak discontinuities in relativistic fluid dynamics 89
4.4 Weak discontinuities in relativistic magneto-fluid dynamics 92
4.5 Electromagnetic and gravitational discontinuities 94
5 Relativistic simple waves 103
5.0 Introduction 103
5.1 General formalism 105
viii Contents
5.2 Simple waves in relativistic fluid dynamics: Eulerian
treatment 109
5.3 One dimensional relativistic fluid dynamics in Lagrangian
coordinates 112
5.4 Simple waves in Lagrangian coordinates 117
5.5 Evaluation of the Riemann invariants for relativistic
acoustic simple waves 120
5.6 General properties of isentropic flow 130
5.7 Unsteady one dimensional and isentropic flow in special
relativity 132
5.8 Stationary potential two dimensional flow in special
relativity 134
5.9 Simple waves in relativistic magneto-fluid dynamics 137
6 Relativistic geometrical optics 157
6.0 Introduction 157
6.1 Geometrical optics in general relativity 160
6.2 Geometrical optics in general relativistic refractive media 165
6.3 Electromagnetic waves in a cold relativistic plasma: linear
theory 170
6.4 Electromagnetic waves in a cold relativistic plasma: weakly
nonlinear analysis 176
7 Relativistic asymptotic waves 188
7.0 Introduction 188
7.1 Asymptotic waves for quasi-linear systems 189
7.2 Asymptotic waves in relativistic fluid dynamics 196
7.3 Asymptotic waves in relativistic magneto-fluid dynamics 199
7.4 Asymptotic and approximate waves for Einstein's
equations in vacuo 202
8 Relativistic shock waves 211
8.0 Introduction 211
8.1 The jump conditions in relativistic fluid dynamics 215
8.2 Solutions of the jump conditions 228
8.3 Relativistic detonation and deflagration waves 244
8.4 The jump conditions in relativistic magneto-fluid dynamics 258
8.5 Evolutionary conditions for relativistic shock waves 273
Contents ix
9 Propagation of relativistic shock waves 276
9.0 Introduction 276
9.1 Damping of plane one dimensional shock waves in a
relativistic fluid 277
9.2 Propagation of weak shock waves 285
10 Stability of relativistic shock waves 289
10.0 Introduction 289
10.1 Linear stability of a relativistic shock 291
10.2 Corrugation stability of a relativistic shock 301
10.3 Further stability considerations 311
10.4 Examples 315
References 325
Index 335