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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 Einstein's 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.
This book provides an introduction to the theory of relativity and
the mathematics used in its processes. Three elements of the book
make it stand apart from previously published books on the theory
of relativity. First, the book starts at a lower mathematical level
than standard books with tensor calculus of sufficient maturity to
make it possible to give detailed calculations of relativistic
predictions of practical experiments. Self-contained introductions
are given, for example vector calculus, differential calculus and
integrations. Second, in-between calculations have been included,
making it possible for the non-technical reader to follow
step-by-step calculations. Thirdly, the conceptual development is
gradual and rigorous in order to provide the inexperienced reader
with a philosophically satisfying understanding of the theory. The
goal of this book is to provide the reader with a sound conceptual
understanding of both the special and general theories of
relativity, and gain an insight into how the mathematics of the
theory can be utilized to calculate relativistic effects.
This book provides an introduction to the theory of relativity and
the mathematics used in its processes. Three elements of the book
make it stand apart from previously published books on the theory
of relativity.
First, the book starts at a lower mathematical level than standard
books with tensor calculus of sufficient maturity to make it
possible to give detailed calculations of relativistic predictions
of practical experiments. Self-contained introductions are given,
for example vector calculus, differential calculus and
integrations. Second, in-between calculations have been included,
making it possible for the non-technical reader to follow
step-by-step calculations. Thirdly, the conceptual development is
gradual and rigorous in order to provide the inexperienced reader
with a philosophically satisfying understanding of the theory.
The goal of this book is to provide the reader with a sound
conceptual understanding of both the special and general theories
of relativity, and gain an insight into how the mathematics of the
theory can be utilized to calculate relativistic effects.
These notes are a transcript of lectures delivered by Oyvind Gron
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, A Frode Hansen and Ragnvald J. Irgens using LT X2 . Svend
E. Hjelmeland has made E many useful suggestions which have
improved the text. I would also like to thank Jon Magne Leinaas and
Sigbjorn Hervik for contributing with problems, and Gorm Krogh
Johnsen for help with nishing 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 bene t particularly
to students of general relativity and look forward to their
comments, we welcome all interested readers and accept all feedback
with thanks. All comment may be sent to the author by e-mail."
This book introduces the general theory of relativity and includes
applications to cosmology. The book provides a thorough
introduction to tensor calculus and curved manifolds. After the
necessary mathematical tools are introduced, the authors offer a
thorough presentation of the theory of relativity. Also included
are some advanced topics not previously covered by textbooks,
including Kaluza-Klein theory, Israel's formalism and branes.
Anisotropic cosmological models are also included. The book
contains a large number of new exercises and examples, each with
separate headings. The reader will benefit from an updated
introduction to general relativity including the most recent
developments in cosmology.
This book introduces the general theory of relativity and
includes applications to cosmology. The book provides a thorough
introduction to tensor calculus and curved manifolds. After the
necessary mathematical tools are introduced, the authors offer a
thorough presentation of the theory of relativity. Also included
are some advanced topics not previously covered by textbooks,
including Kaluza-Klein theory, Israel's formalism and branes.
Anisotropic cosmological models are also included. The book
contains a large number of new exercises and examples, each with
separate headings. The reader will benefit from an updated
introduction to general relativity including the most recent
developments in cosmology.
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