Dynamical and Hamiltonian Formulation of General Relativity

Einstein’s theory of General Relativity describes spacetime as a solution of a set of non-linear partial differential equations. These equations are initially not in the form of evolution equations and it is hence not clear how to formulate and solve init

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Handbook Spacetime



Ashtekar Petkov Editors

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Springer Handbook of Spacetime

Springer Handbooks provide a concise compilation of approved key information on methods of research, general principles, and functional relationships in physical and applied sciences. The world’s leading experts in the fields of physics and engineering will be assigned by one or several renowned editors to write the chapters comprising each volume. The content is selected by these experts from Springer sources (books, journals, online content) and other systematic and approved recent publications of scientific and technical information. The volumes are designed to be useful as readable desk reference book to give a fast and comprehensive overview and easy retrieval of essential reliable key information, including tables, graphs, and bibliographies. References to extensive sources are provided.

Springer

Handbook of Spacetime

Abhay Ashtekar, Vesselin Petkov (Eds.) With 190 Figures and 9 Tables

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Editors Abhay Ashtekar Pennsylvania State University Department of Physics University Park PA 16802, USA Vesselin Petkov Institute for Foundational Studies Hermann Minkowski Montreal, Quebec, Canada

ISBN: 978-3-642-41991-1 e-ISBN: 978-3-642-41992-8 DOI 10.1007/978-3-642-41992-8 Springer Dordrecht Heidelberg London New York Library of Congress Control Number:

2014940760

© Springer-Verlag Berlin Heidelberg 2014 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 microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under 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 this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Production and typesetting: le-tex publishing services GmbH, Leipzig Senior Manager Springer Handbook: Dr. W. Skolaut, Heidelberg Typography and layout: schreiberVIS, Seeheim Illustrations: Hippmann GbR, Schwarzenbruck Cover design: eStudio Calamar Steinen, Barcelona Cover production: WMXDesign GmbH, Heidelberg Printing and binding: Stürtz GmbH, Würzburg Printed on acid free paper Springer is part of Springer Science+Business Media (www.springer.com)

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Preface

In his Principia Mathematica, Isaac Newton formalized the notions of space and time, thereby laying the foundations of a new, revolutionary science. The sweeping success of celestial mechanics firmly established the power of Newton’s spacetime paradigm. Soon it became firmly rooted in scientific thought and it gradually came to b