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Lecture Notes on the General Theory of Relativity: From Newton's Attractive Gravity to the Repulsive Gravity of Vacuum Energy (Lecture Notes in Physics) Hardcover – 21 Apr 2009


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From the reviews:

“The textbook is self-contained and designed for master students. The book provides an introduction to abstract notations for tensor calculus and differential geometry, in particular the calculus of differential forms.” (Vladimir Dzhunushaliev, Zentralblatt MATH, Vol. 1192, 2010)

“This book collects the lecture notes of a course on general relativity … . The text is enriched by a collection of interesting and stimulating exercises, which both allow a working knowledge of the theory and provide further insight into the theory itself and its applications as well. Together with the personal didactical approach taken by the author in his book, these exercises may represent useful hints for a teacher wishing to introduce new ideas in a standard introductory course on general relativity.” (Giovanni Preti, Mathematical Reviews, Issue 2011 k)

From the Back Cover

This book has resulted from a course in the general theory of relativity at the University of Oslo where the author has lectured for more than twenty years. Although the text is designed for master students, it is rather self-contained. Since mathematics courses on differential geometry and tensor calculus usually employ a rather abstract notation different from the component notation used in physical applications, the book introduces not only an introduction to the physical principles of the theory and physical applications of the theory, but also introduces the mathematics which is needed, in particular the calculus of differential forms. Detailed calculations are given of the bending of light, the perihelion precession of Mercury and the predictions for the Hafele-Keating experiment. The Tolman-Oppenheimer-Volkoff equation is deduced and solved for an incompressible fluid to give the internal Schwarzschild solution. Rotating black holes are discussed. The Friedmann-Robertson-Walker universe models are deduced. Also the reader will become familiar with the Universe model which is now considered as the standard model of the universe; a flat model filled with vacuum energy and cold matter. The inflationary era at the first moment of the history of our universe is also discussed.


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Amazon.com: 2 reviews
4 of 4 people found the following review helpful
G1 and G2 are correct -- it's a fantastic book -- buy it! 9 Nov. 2010
By Nils K. Oeijord - Published on Amazon.com
Format: Hardcover
The first reviewer is absolutely wrong. G1 and G2 are absolutely correct.

The reviewer does not know that the laws of nature are written
as tensor equations and so are independent of the
coordinate system used. The coordinate system can be in any kind of motion. The laws are the same. It's terrible to claim, as the reviewer does, that the laws of nature are dependent on the type
of coordinate system used.

The reviewer do you not understand the principle of equivalence since he wrongly says that G2 is wrong.

The reviewer is also wrong regarding the twin paradox. The twin
paradox is not a paradox in GR, only in SR. To fully explain
(and calculate numerically, of course) the twin paradox we
MUST use GR.

This book is probably the best book to easily learn basic general
relativity. It's probably the best book for self-study of GR.

Buy it. It's fantastic! The small steps in the theory make you
read and understand this text much, much faster than any other
GR book does. This is the only book you need. But of course there are certain minimum prerequisites when it comes to the reader's
knowledge of basic mathematics, such as calculus, linear algebra,
etc.

NKO
4 of 7 people found the following review helpful
Some serious errors in describing the General Relativity! 4 April 2010
By ANDREJS JANSONS - Published on Amazon.com
Format: Hardcover Verified Purchase
Quite unfortunately, in this overall well written book the author makes some serious mistakes regarding the essence of the GR. For instance:

1. On the page 10, the author states that in non-inertial
frames the following postulates apply:

"G1. The laws of nature are the same in all reference frames."

"G2. An observer with arbitrary motion may consider himself
to be at rest and the environment as moving."

The both statements, especially G2, are incorrect. An observer
in an accelerated frame definitely can tell that he is
in an accelerated frame, because, for instance, he will be
feeling g-forces, the period of a pendulum will be changing
from the magnitude of the acceleration, etc., quite different
from an inertial (non-accelerated) frame, where everything
will be floating in weightlessness! The correct statement,
describing the equivalence principle is:

"An observer in an uniformly accelerated frame may consider
himself to be at rest in a frame with an uniform gravitational
field. The laws of nature are the same in the both frames."

Since "uniform" gravitational fields do not exist in the
nature (except as an approximation in a very small volume),
Einstein came to the concept of space-time curvature expressing
the "real" gravitational field, etc.

Because of this initial error, on the page 33 the author,
when explaining the (in)famous "twin paradox" concludes
"In order to arrive at a clear answer to these questions,
we shall have to use the result from the general theory
of relativity." This statement is absolutely false, as it
had been shown countless times before in various texts, as
long as the "real" gravitational field is not present
(the Riemann tensor equal to 0), the twin paradox can be
easily resolved using only the special theory of relativity
(see the book by Taylor and Wheeler)! This argument has already
been discussed to death, so it's quite bad to open it anew
in this book :-(
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