A Short Course in General Relativity

1. Front Matter

   Pages i-ix

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2. Introduction

   • James Foster, J. David Nightingale

   Pages 1-6

3. Vector and tensor fields

   • James Foster, J. David Nightingale

   Pages 7-54

4. The spacetime of general relativity and paths of particles

   • James Foster, J. David Nightingale

   Pages 55-98

5. Field equations and curvature

   • James Foster, J. David Nightingale

   Pages 99-123

6. Physics in the vicinity of a massive object

   • James Foster, J. David Nightingale

   Pages 124-160

7. Gravitational radiation

   • James Foster, J. David Nightingale

   Pages 161-175

8. Elements of cosmology

   • James Foster, J. David Nightingale

   Pages 176-189

9. Back Matter

   Pages 190-250

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Suitable as a one-semester course in general relativity for senior undergraduate or beginning graduate students, this text clarifies the mathematical aspects of Einstein's general theory of relativity without sacrificing physical understanding. The text begins with an exposition of those aspects of tensor calculus and differential geometry needed for a proper exposition of the subject. The discussion then turns to the spacetime of general relativity and to geodesic motion, comparisons and contrasts with Newton's theory being drawn where appropriate. A brief consideration of the field equations is followed by a discussion of physics in the vicinity of massive objects, including an elementary treatment of black holes. Particular attention is paid to those aspects of the theory that have observational consequences. The book concludes with brief introductory chapters on gravitational radiation and cosmology, and includes an appendix that reviews the special theory of relativity. In preparing this new edition, the authors have made extensive revisions to the original text. In particular, the first three chapters -- covering coordinate systems, tensors and the geometry of curved spaces -- have been completely rewritten to make the material readily accessible to physics students. Many examples, exercises and problems help guide the student through the theory.

• 4-vector
• EFE
• Gravity
• Lorentz transformation
• Relativity
• Special relativity
• Time dilation
• general relativity
• general theory of relativity
• special theory of relativity

From the reviews of the third edition:

"This is the third edition of a book that is already familiar to those who teach an introductory course in general relativity. … Important concepts are introduced slowly and carefully, so that the resulting text is a comprehensible first introduction that is suitable for both physics and mathematics students. … its strength is that it is a short introduction to the subject that still covers all the essential material for a first course and provides a sound basis for further study." (J. B. Griffiths, Mathematical Reviews, Issue 2006 h)

"This book is a well-developed introduction to General Relativity. … the present third edition is really re-worked in many places in comparison with the previous ones. … Three appendices are quite helpful … . Solutions to the exercises, References and Index close this very readable book. … Every chapter ends with a list of problems … ." (Hans-Jürgen Schmidt, Zentralblatt MATH, Vol. 1089 (15), 2006)

• School of Mathematical Sciences, University of Sussex, Falmer, Brighton, UK

  James Foster

• Department of Physics, The College at New Paltz, State University of New York, New Paltz, USA

  J. David Nightingale

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