Introduction to Einstein’s Theory of Relativity

1. Front Matter

   Pages i-xxiv

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2. Newton’s Theory of Gravitation

   • Øyvind Grøn

   Pages 1-22

3. The Special Theory of Relativity

   • Øyvind Grøn

   Pages 23-58

4. Vectors, Tensors and Forms

   • Øyvind Grøn

   Pages 59-87

5. Accelerated Reference Frames

   • Øyvind Grøn

   Pages 89-118

6. Covariant Differentiation

   • Øyvind Grøn

   Pages 119-172

7. Curvature

   • Øyvind Grøn

   Pages 173-196

8. Einstein’s Field Equations

   • Øyvind Grøn

   Pages 197-210

9. Schwarzschild Spacetime

   • Øyvind Grøn

   Pages 211-242

10. The Linear Field Approximation and Gravitational Waves

    • Øyvind Grøn

    Pages 243-269

11. Black Holes

    • Øyvind Grøn

    Pages 271-282

12. Sources of Gravitational Fields

    • Øyvind Grøn

    Pages 283-309

13. Cosmology

    • Øyvind Grøn

    Pages 311-391

14. Back Matter

    Pages 393-520

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The revised and updated 2^nd 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.

• Lorentz contraction and transformation
• Coordinate Systems and Minkowski diagrams
• Accelerating and rotating reference frames
• Time dilation
• textbook on general theory of relativity
• textbook on special theory of relativity
• introduction to Newtonian gravity
• Introduction to gravitational waves
• The twin paradox
• Gravitational Doppler effect
• Covariant differentiation of vectors, forms and tensors
• Einstein's field equations
• The Schwarzschild spacetime
• Introduction to black hole physics
• Gravitational waves explained

• OsloMet—Oslo Metropolitan University, Oslo, Norway

  Øyvind Grøn

Øyvind Grøn is a Norwegian physicist, who took the cand. real. degree at the University of Oslo in 1973, majoring in meteorology, and went on to obtain the PhD degree in 1990 with a thesis on repulsive gravitation. He was appointed as a professor at Oslo University College in 1994, having been an associate professor since 1985, and has also been professor at the University of Oslo since 1994. Grøn has conducted research within the areas of general relativity, cosmology and classical electromagnetism. He has thrown new light on themes like the twin paradox, physics in a rotating reference system (Ehrenfest paradox) and repulsive gravitation associated with vacuum energy. He has written several books including Introduction to General Relativity and its Mathematics (Springer 1998, with Arne Næss), Einstein's General Theory of Relativity: With Modern Applications in Cosmology (Springer 2007, with Sigbjørn Hervik) and Einstein's Theory: A Rigorous Introduction for the Mathematically Untrained (Springer 2011, with Arne Næss)

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