General Relativity Without Calculus A Concise Introduction to the Ge
“General Relativity Without Calculus” offers a compact but mathematically correct introduction to the general theory of relativity, assuming only a basic knowledge of high school mathematics and physics. Targeted at first year undergraduates (and advanced
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Undergraduate Lecture Notes in Physics (ULNP) publishes authoritative texts covering topics throughout pure and applied physics. Each title in the series is suitable as a basis for undergraduate instruction, typically containing practice problems, worked examples, chapter summaries, and suggestions for further reading. ULNP titles must provide at least one of the following: • An exceptionally clear and concise treatment of a standard undergraduate subject. • A solid undergraduate-level introduction to a graduate, advanced, or nonstandard subject. • A novel perspective or an unusual approach to teaching a subject. ULNP especially encourages new, original, and idiosyncratic approaches to physics teaching at the undergraduate level. The purpose of ULNP is to provide intriguing, absorbing books that will continue to be the reader’s preferred reference throughout their academic career.
José Natário
General Relativity Without Calculus A Concise Introduction to the Geometry of Relativity
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José Natário Departamento de Matematica Instituto Superior Tecnico Av. Rovisco Pais 1049-001 Lisbon Portugal e-mail: [email protected]
ISSN 2192-4791 ISBN 978-3-642-21451-6 DOI 10.1007/978-3-642-21452-3
e-ISSN 2192-4805 e-ISBN 978-3-642-21452-3
Springer Heidelberg Dordrecht London New York Springer-Verlag Berlin Heidelberg 2011 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. Cover design: eStudio Calamar, Berlin/Figueres Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To my uncle Joaquim, who first told me how far the stars really are, and to my father, my first and best teacher
Preface
This book was written as a guide for a one-week course aimed at exceptional students in their final years of secondary education, taught in July 2005, and again in July 2010, at the Mathematics Department of Instituto Superior Técnico (Lisbon). The course was intended to provide a quick but nontrivial introduction to Einstein’s general theory of relativity, in which the beauty of the interplay between geometry and physics would be apparent. Given the audience, there was the limitation of using only elementary mathematics and physics; due
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