Lecture Notes on the General Theory of Relativity: From Newton’s Attractive Gravity to the Repulsive Gravity of Vacuum Energy (Lecture Notes in Physics Book 772)

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. Front Matter....Pages i-xvii Newton’s Law of Universal Gravitation....Pages 1-16 The Special Theory of Relativity....Pages 17-49 Vectors, Tensors and Forms....Pages 51-75 Accelerated Reference Frames....Pages 77-96 Covariant Differentiation....Pages 97-132 Curvature....Pages 133-147 Einstein’s Field Equations....Pages 149-157 The Schwarzschild Spacetime....Pages 159-185 Black Holes....Pages 187-198 Schwarzschild’s Interior Solution....Pages 199-206 Cosmology....Pages 207-244 Back Matter....Pages 245-248 This book collects lectures on the general theory of relativity given by Dr. Øyvind Grøn at the University of Oslo, Norway. This accessible text allows students to follow the deductions all the way throughout the book. 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. Ø. Grøn. Includes Bibliographical References And Index.