Oscillations and Waves in Strong Gravitational and Electromagnetic F
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
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W. Beiglbock J.L. Birman R.P. Geroch E.H. Lieb T. Regge W. Thirring Series Editors
Nail R.Sibgatullin
Oscillations and Waves in Strong Gravitational and Electromagnetic Fields
With 26 Figures
Spri nger-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona
Professor Dr. Nail R. Sibgatullin Faculty of Mechanics and Mathematics, Moscow State University SU-119899 Moscow, USSR
Translator: Dr. Nathaniel M. Queen Department of Mathematics, The University of Birmingham P.O. Box 363, Birmingham B15 2IT, United Kingdom
Editors Wolf Beiglb6ck
Elliott H. Lieb
Institut fiir Angewandte Mathematik Universitiit Heidelberg 1m Neuenheimer Feld 294 D-6900 Heidelberg 1 Fed. Rep. of Germany
Department of Physics Joseph Henry Laboratories Princeton University Princeton,NJ08540, USA
Joseph L. Birman
Tullio Regge
Department of Physics, The City College of the City University of New York New York, NY 10031, USA
Istituto di Fisca Teorica Universita di Torino, C. so M. d'Azeglio, 46 1-10125 Torino, Italy
Robert P. Geroch
Walter Thirring
Enrico Fermi Institute University of Chicago 5640 EllisAve. Chicago, IL 60637, USA
Institut fiirTheoretische Physik der UniversitiitWien, Boltzmanngasse 5 A-1090Wien, Austria
Title of the original Russian edition: Kolebaniya i volny v silnykh gravitatsionnykh i elektromagnitnykh polyakh © Nauka, Moscow 1984
ISBN-13: 978-3-642-83529-2 DOl: 10.1007/978-3-642-83527-8
e-ISBN-13: 978-3-642-83527-8
Library of Congress Cataloging·in·Publication Data. Sib~atullin, N. R. (Nail' Rakhimovich) [KolebaniG i volny v sil 'nykh gravitatsionnykh i elektromagnitnykh pohakh. English 1Oscillations and waves in strong gravitational and electromagnetic fields / Nail R. Sibgatullin. p. cm.-(Texts and monographs in physics) Translation of: Kolebani2. i volny sil 'nykh gravitatsionnykh i elektromagnitnykh polGkh. Includes bibliographical references. ISBN 0-387-19461-4 (U.S.) 1. Gravitational fields. 2. Electromagnetic fields. 3. Perturbation (Quantum dynamics) I. Title. II. Series. QB283.S5513 1990 530.1 '4-dc20 89-11542 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions ofthe German Copyright Law of September 9,1965, in its current version, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. 04.>2 - 4.>1 }, H2 - E2 + 2iE . H = 4(4.>04.>2 - 4.>~) . Let us consider now the algebra of a fourth-rank tensor Rijkl which is antisymmetric in the first and second indices, and also in the third and fourth indices, and symmetric with respect to transpositions of the first and second pairs of indices. Contracting the components of Rijkl with respect to the first and third indices, we obtain a symmetric second-rank tensor R