Undergraduate Texts in Physics
Series Editors
Kurt H. Becker
NYU Polytechnic School of Engineering, Brooklyn, NY, USA
Jean-Marc Di Meglio
Matire et Systmes Complexes, Universit Paris Diderot, Btiment Condorcet, Paris, France
Sadri D. Hassani
Department of Physics, Loomis Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL, USA
Morten Hjorth-Jensen
Department of Physics, Blindern, University of Oslo, Oslo, Norway
Michael Inglis
Patchogue, NY, USA
Bill Munro
NTT Basic Research Laboratories, Optical Science Laboratories, Atsugi, Kanagawa, Japan
Susan Scott
Department of Quantum Science, Australian National University, Acton, ACT, Australia
Martin Stutzmann
Walter Schottky Institute, Technical University of Munich, Garching, Bayern, Germany
Undergraduate Texts in Physics (UTP) publishes authoritative texts covering topics encountered in a physics undergraduate syllabus. Each title in the series is suitable as an adopted text for undergraduate courses, typically containing practice problems, worked examples, chapter summaries, and suggestions for further reading. UTP titles should provide an exceptionally clear and concise treatment of a subject at undergraduate level, usually based on a successful lecture course. Core and elective subjects are considered for inclusion in UTP.
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yvind Grn
OsloMetOslo Metropolitan University, Oslo, Norway
ISSN 2510-411X e-ISSN 2510-4128
Undergraduate Texts in Physics
ISBN 978-3-030-43861-6 e-ISBN 978-3-030-43862-3
https://doi.org/10.1007/978-3-030-43862-3
1st edition: Springer Science+Business Media, LLC 2009
Springer Nature Switzerland AG 2020
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Preface to the Second Edition
These notes are a transcript of lectures delivered by yvind Grn during the spring of 1997 at the University of Oslo. The manuscript has been revised in 2019. The present version of this document is an extended and corrected version of a set of Lecture Notes which were written down by S. Bard, Andreas O. Jaunsen, Frode Hansen and Ragnvald J. Irgens using . Sven E. Hjelmeland has made many useful suggestions which have improved the text.
The manuscript has been revised in 2019. In this version, solutions to the exercises have been included. Most of these have been provided by Hkon Enger. I thank all my good helpers for enthusiastic work which was decisive for the realization of the book.
I hope that these notes are useful to students of general relativity and look forward to their comments accepting all feedback with thanks. The comments may be sent to the author by e-mail to oyvind.gron.no@gmail.com.
yvind Grn
Oslo, Norway
Preface to the First Edition
These notes are a transcript of lectures delivered by yvind Grn during the spring of 1997 at the University of Oslo.
The present version of this document is an extended and corrected version of a set of Lecture Notes which were typesetted by S. Bard, Andreas O. Jaunsen, Frode Hansen and Ragnvald J. Irgens using . Svend E. Hjelmeland has made many useful suggestions which have improved the text. I would also like to thank Jon Magne Leinaas and Sigbjrn Hervik for contributing with problems and Gorm Krogh Johnsen for help with finishing the manuscript. I also want to thank Prof. Finn Ravndal for inspiring lectures on general relativity.
While we hope that these typeset notes are of benefit particularly to students of general relativity and look forward to their comments, we welcome all interested readers and accept all feedback with thanks.
All comments may be sent to the author by e-mail.
E-mail: Oyvind.Gron@iu.hio.no
yvind Grn
List of Definitions
Definition 3.1.1 Four-velocity
Definition 3.1.2 Four-momentum
Definition 3.1.3 Minkowski force
Definition 3.1.4 Four-acceleration
Definition 3.1.5 Reference frame
Definition 3.1.6 Coordinate system
Definition 3.1.7 Co-moving coordinate system
Definition 3.1.8 Orthonormal basis
Definition 3.1.9 Preliminary definition of coordinate basis vector
Definition 3.1.10 General definition of coordinate basis vectors
Definition 3.1.11 Orthonormal basis
Definition 3.1.12 Commutator of vectors
Definition 3.1.13 Structure coefficients
Definition 3.2.1 One-form basis
Definition 3.2.2 Tensors
Definition 3.2.3 Tensor product
Definition 3.2.4 The scalar product
Definition 3.2.5 The metric tensor
Definition 3.2.6 Contravariant components of the metric tensor
Definition 3.4.1 Antisymmetric tensor
Definition 3.4.2p-form
Definition 3.4.3 The wedge product
Definition 4.9.1 Born-rigid Motion
Definition 4.10.1 The Projection Tensor
Definition 5.2.1 Christoffel symbols
Definition 5.2.2 Covariant directional derivative