Lecture Notes on the General Theory of Relativity

From Newton's Attractive Gravity to the Repulsive Gravity of Vacuum Energy

  • Øyvind Grøn

Part of the Lecture Notes in Physics book series (LNP, volume 772)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Øyvind Grøn
    Pages 1-16
  3. Øyvind Grøn
    Pages 17-49
  4. Øyvind Grøn
    Pages 51-75
  5. Øyvind Grøn
    Pages 77-96
  6. Øyvind Grøn
    Pages 97-132
  7. Øyvind Grøn
    Pages 133-147
  8. Øyvind Grøn
    Pages 149-157
  9. Øyvind Grøn
    Pages 159-185
  10. Øyvind Grøn
    Pages 187-198
  11. Øyvind Grøn
    Pages 199-206
  12. Øyvind Grøn
    Pages 207-244
  13. Back Matter
    Pages 245-248

About this book


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.


EFE Four-vector Gravity Lorentz transformation Minkowski diagram RMS Redshift Relativity Sagnac effect Time dilation general theory of relativity special theory of relativity

Authors and affiliations

  • Øyvind Grøn
    • 1
  1. 1.Faculty of EngineeringOslo University CollegeOsloNorway

Bibliographic information