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Øyvind Grøn - Introduction to Einstein’s Theory of Relativity: From Newton’s Attractive Gravity to the Repulsive Gravity of Vacuum Energy

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Øyvind Grøn Introduction to Einstein’s Theory of Relativity: From Newton’s Attractive Gravity to the Repulsive Gravity of Vacuum Energy
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Introduction to Einstein’s Theory of Relativity: From Newton’s Attractive Gravity to the Repulsive Gravity of Vacuum Energy: summary, description and annotation

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The revised and updated 2nd edition of this established textbook provides a self-contained introduction to the general theory of relativity, describing not only the physical principles and applications of the theory, but also the mathematics needed, in particular the calculus of differential forms.Updated throughout, the book contains more detailed explanations and extended discussions of several conceptual points, and strengthened mathematical deductions where required. It includes examples of work conducted in the ten years since the first edition of the book was published, for example the pedagogically helpful concept of a river of space and a more detailed discussion of how far the principle of relativity is contained in the general theory of relativity. Also presented is a discussion of the concept of the gravitational field in Einsteins theory, and some new material concerning the twin paradox in the theory of relativity.Finally, the book contains a new section about gravitational waves, exploring the dramatic progress in this field following the LIGO observations.Based on a long-established masters course, the book serves advanced undergraduate and graduate level students, and also provides a useful reference for researchers.

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Undergraduate Texts in Physics Series Editors Kurt H Becker NYU Polytechnic - photo 1
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.

UTP books will be ideal candidates for course adoption, providing lecturers with a firm basis for development of lecture series, and students with an essential reference for their studies and beyond.

More information about this series at http://www.springer.com/series/15593

yvind Grn
Introduction to Einsteins Theory of Relativity
From Newtons Attractive Gravity to the Repulsive Gravity of Vacuum Energy
2nd ed. 2020
yvind Grn OsloMetOslo Metropolitan University Oslo Norway ISSN 2510-411X - photo 2
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
This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed.
The use of general descriptive names, registered names, trademarks, service marks, 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.
The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This Springer imprint is published by the registered company Springer Nature Switzerland AG

The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

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 - photo 3 . 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 - photo 4 . 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
Contents
List of Figures
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
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