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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.
List of contents
Newton's Law of Universal Gravitation.- The Special Theory of Relativity.- Vectors, Tensors and Forms.- Accelerated Reference Frames.- Covariant Differentiation.- Curvature.- Einstein's Field Equations.- The Schwarzschild Spacetime.- Black Holes.- Schwarzschild's Interior Solution.- Cosmology.
Summary
This book collects lectures on the general theory of relativity given by Dr. Oyvind Gron at the University of Oslo, Norway. This accessible text allows students to follow the deductions all the way throughout the book.
Additional text
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)
Report
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)
