A Short Course In General Relativity

A Short Course in General Relativity Third Edition James Foster 1. David Nightingale A Short Course in General Relativity Third Edition With 51 Illustrations ~ Springer James Foster formerly Senior Lecturer in Mathematics University of Sussex Brighton UK 1. David Nightingale Emeritus Professor of Physics State University of New York New Paltz, NY USA Library of Congress Control Number: 2005927384 ISBN-lO : 0-387-26078-1 ISBN-13 : 978-0387-26078-5 e-ISBN 0-387-27583-5 Printed on acid-free paper. © 2006, 1994 Springer Science+Business Media , Inc . All rights reserved. This work may not be tran slated or copied in whole or in part without the written permi ssion of the publisher (Springer Science-Business Media, Inc., 233 Spring Street, New York, NY 10013, USA) , except for brief excerpts in connection with reviews or scholarly anal ysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden . The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opin ion as to whether or not they are subject to proprietary rights. Printed in the United States of America . 987654321 springeronline.com (EB) Preface This book is a short introduction to general relativity, intended primarily as a one-semester course for first-year graduate students (or for seniors) in physics, or in related subjects such as astrophysics. While we expect such students to have been exposed to special relativity in their introductory modern physics courses (most likely in their sophomore year) it is unlikely that they have used the standard 4-vector methods, and so we supply such a review in Appendix A. We strongly advise reading Appendix A first . Most students approaching general relativity require an introduction to tensors, and these are dealt with in Chapter 1 and the first half of Chapter 2, where geodesics, absolute and covariant differentiation, and parallel transport are discussed. This enables us to discuss th e spacetime of general relativity in the latter half of the chapter and takes us on to a discussion of the field equations in Chapter 3. In Chapter 4 the results learned are applied to physics in the vicinity of a massive object , where we have tried to compare general relativistic results with their Newtonian counterparts. Chapters 5 and 6, on gravitational radiation and the elements of cosmology, respectively, give further applications of the theory, but students wanting a more detailed knowledge of these topics (and indeed all topics) would have to turn to the texts referred to in the body of the book . Over the years, a version of this course has been offered variously (by JDN) at the University of Mississippi (Ole Miss), at Bard College, and at SUNY New Paltz, as well as (by JF) at the University of Sussex. It was often found that there was not enough time for Chapters 5 and 6, unless one made judicious cuts elsewhere . A few cuts may be made in the first two chapters, but it would probably be better to omit either Chapter 5, or Chapter 6