中外物理学精品书系·引进系列49【英文原版替代】-广义相对论的3+1形式:数值相对论基础(影印版)-[法]E·古尔古隆-Springer出版-2012.pdf
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1、Lecture Notes in Physics Volume 846 Founding Editors W. Beiglbck J. Ehlers K. Hepp H. Weidenmller Editorial Board B.-G. Englert, Singapore U. Frisch, Nice, France F. Guinea, Madrid, Spain P. Hnggi, Augsburg, Germany W. Hillebrandt, Garching, Germany M. Hjorth-Jensen, Oslo, Norway R. A. L. Jones, She
2、feld, UK H. von Lhneysen, Karlsruhe, Germany M. S. Longair, Cambridge, UK M. Mangano, Geneva, Switzerland J.-F. Pinton, Lyon, France J.-M. Raimond, Paris, France A. Rubio, Donostia-San Sebastin, Spain M. Salmhofer, Heidelberg, Germany D. Sornette, Zurich, Switzerland S. Theisen, Potsdam, Germany D.
3、Vollhardt, Augsburg, Germany W. Weise, Garching, Germany For further volumes: http:/ Lecture Notes in Physics The series Lecture Notes in Physics (LNP), founded in 1969, reports new developments in physics research and teachingquickly and informally, but with a high quality and the explicit aim to s
4、ummarize and communicate current knowledge in an accessible way. Books published in this series are conceived as bridging material between advanced graduate textbooks and the forefront of research and to serve three purposes: to be a compact and modern up-to-date source of reference on a well-dened
5、topic to serve as an accessible introduction to the eld to postgraduate students and nonspecialist researchers from related areas to be a source of advanced teaching material for specialized seminars, courses and schools Both monographs and multi-author volumes will be considered for publication. Ed
6、ited volumes should, however, consist of a very limited number of contributions only. Proceedings will not be considered for LNP. Volumes published in LNP are disseminated both in print and in electronic formats, the electronic archive being available at . The series content is indexed, abstracted a
7、nd referenced by many abstracting and information services, bibliographic networks, subscription agencies, library networks, and consortia. Proposals should be sent to a member of the Editorial Board, or directly to the managing editor at Springer: Christian Caron Springer Heidelberg Physics Editori
8、al Department I Tiergartenstrasse 17 69121 Heidelberg/Germany ric Gourgoulhon 3+1 Formalism in General Relativity Bases of Numerical Relativity 123ric Gourgoulhon Lab. Univers et Thories (LUTH) UMR 8102 du CNRS Observatoire de Paris Universit Paris Diderot place Jules Janssen 5 92190 Meudon France I
9、SSN 0075-8450 e-ISSN 1616-6361 ISBN 978-3-642-24524-4 e-ISBN 978-3-642-24525-1 DOI 10.1007/978-3-642-24525-1 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2011942212Springer-Verlag Berlin Heidelberg 2012 This work is subject to copyright. All rights are reserved,
10、whether the whole or part of the material is concerned, specically the rights of translation, reprinting, reuse of illustrations, recitation, broadcast- ing, reproduction on microlm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only und
11、er the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in t
12、his publication does not imply, even in the absence of a specic statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Printed on acid-free paper Springer is part of Springer Science+Business Media ()To the memory of Jean-Alain Mar
13、ck (1955-2000)Preface This monograph originates from lectures given at the General Relativity Trimester at the Institut Henri Poincar in Paris 1; at the VII Mexican School on Gravi- tation and Mathematical Physics in Playa del Carmen (Mexico) 2; and at the 2008 International Summer School on Computa
14、tional Methods in Gravitation and Astrophysics held in Pohang (Korea) 3. It is devoted to the 3+1 formalism of general relativity, which constitutes among other things, the theoretical founda- tions for numerical relativity. Numerical techniques are not covered here. For a pedagogical introduction t
15、o them, we recommend instead the lectures by Choptuik 4 (nite differences) and the review article by Grandclment and Novak 5 (spectral methods), as well as the numerical relativity textbooks by Alcubierre 6, Bona, Palenzuela-Luque and Bona-Casas 7 and Baumgarte and Shapiro 8. The prerequisites are t
16、hose of a general relativity course, at the undergraduate or graduate level, like the textbooks by Hartle 9 or Carroll 10, or part I of Walds book 11, as well as track 1 of the book by Misner, Thorne and Wheeler 12. The fact that the present text consists of lecture notes implies two things: the cal
17、culations are rather detailed (the experienced reader might say too detailed), with an attempt to made them self-consistent and complete, trying to use as infrequently as possible the famous phrases as shown in paper XXX or see paper XXX for details; the bibliographical references do not constitute
18、an extensive survey of the lit- erature on the subject: articles have been cited in so far as they have a direct connection with the main text. The book starts with a chapter setting the mathematical background, which is differential geometry, at a basic level (Chap. 2). This is followed by two pure
19、ly geometrical chapters devoted to the study of a single hypersurface embedded in spacetime (Chap. 3) and to the foliation (or slicing) of spacetime by a family of spacelike hypersurfaces (Chap. 4). The presentation is divided in two chapters to distinguish between concepts which are meaningful for
20、a single hypersurface and those that rely on a foliation. The decomposition of the Einstein equation relative viito the foliation is given in Chap. 5, giving rise to the Cauchy problem with constraints, which constitutes the core of the 3+1 formalism. The ADM Hamil- tonian formulation of general rel
21、ativity is also introduced in this chapter. Chapter 6 is devoted to the decomposition of the matter and electromagnetic eld equations, focusing on the astrophysically relevant cases of a perfect uid and a perfect conductor (ideal MHD). An important technical chapter occurs then: Chap. 7 introduces s
22、ome conformal transformation of the 3-metric on each hypersurface and the corresponding rewriting of the 3+1 Einstein equations. As a by-product, we also discuss the Isenberg-Wilson-Mathews (or conformally at) approximation to general relativity. Chapter 8 details the various global quantities assoc
23、iated with asymptotic atness (ADM mass, ADM linear momentum and angular momentum) or with some symmetries (Komar mass and Komar angular momentum). In Chap. 9, we study the initial data problem, presenting with some examples two classical methods: the conformal transversetraceless method and the conf
24、ormal thin-sandwich one. Both methods rely on the conformal decomposition that has been introduced in Chap. 7. The choice of spacetime coordinates within the 3+1 framework is discussed in Chap. 10, starting from the choice of foliation before discussing the choice of the three coordinates in each le
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