© 2019

Elements of General Relativity

  • Concise modern introduction to the mathematical tools

  • Precise mathematical treatment of all problems addressed

  • Can be used for an introductory course on a mathematically-minded introduction to Einstein’s theory of gravitation


Part of the Compact Textbooks in Mathematics book series (CTM)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Piotr T. Chruściel
    Pages 37-49
  3. Piotr T. Chruściel
    Pages 51-117
  4. Piotr T. Chruściel
    Pages 119-165
  5. Piotr T. Chruściel
    Pages 167-187
  6. Piotr T. Chruściel
    Pages 189-249
  7. Back Matter
    Pages 251-283

About this book


This book provides an introduction to the mathematics and physics of general relativity, its basic physical concepts, its observational implications, and the new insights obtained into the nature of space-time and the structure of the universe. It introduces some of the most striking aspects of Einstein's theory of gravitation: black holes, gravitational waves, stellar models, and cosmology. It contains a self-contained introduction to tensor calculus and Riemannian geometry, using in parallel the language of modern differential geometry and the coordinate notation, more familiar to physicists. The author has strived to achieve mathematical rigour, with all notions given careful mathematical meaning, while trying to maintain the formalism to the minimum fit-for-purpose. Familiarity with special relativity is assumed.

The overall aim is to convey some of the main physical and geometrical properties of Einstein's theory of gravitation, providing a solid entry point to further studies of the mathematics and physics of Einstein equations.


general relativity black holes cosmology weak gravitational fields gravitational waves tensor calculus Riemannian geometry Einstein equations

Authors and affiliations

  1. 1.Faculty of PhysicsUniversity of ViennaViennaAustria

About the authors

Piotr T. Chruściel is Professor of Gravitational Physics at the Faculty of Physics of the University of Vienna, where he heads the gravitational physics group. His previous academic postings include the University of Oxford, where he was a lecturer with title of Professor at the Mathematical Institute and a Fellow of Hertford College. He is a Life Member of Clare Hall, Cambridge. He is a specialist in all aspects of mathematical general relativity.

Bibliographic information