A First Course in General Relativity

Praise for the second edition: 'Bernard Schutz's textbook A First Course in General Relativity quickly became a classic, notable for its use of the geometrical approach to the subject, combined with a refreshing succinctness. Since its first publication in 1985, the field of general relativity has exploded ... Schutz has done a masterful job of incorporating these new developments into a revised edition, which is sure to become a new 'classic'.' Clifford M. Will, McDonnell Center for the Space Sciences, Washington University, St. Louis

Praise for the second edition: 'This new edition retains all of the original's clarity and insight into the mathematical foundations of general relativity, but thoroughly updates the accounts of the application of the theory in astrophysics and cosmology. The result is an indispensable volume and this new edition will no doubt become a classic text in its own right.' Mike Hobson, Cavendish Laboratory, University of Cambridge

Praise for the second edition: 'Schutz has updated his eminently readable and eminently teachable A First Course in General Relativity. This text will be appreciated by any upper-level undergraduate with an interest in cosmology, astrophysics, or experimentation in gravitational physics.' Richard Matzner, The Center for Relativity, University of Texas at Austin

Praise for the second edition: ' ... marvellous ... very clear ... I cannot recommend this book highly enough to any physicist who wants a good introduction to general relativity.' David Burton, The Observatory

Praise for the first edition: 'Schutz has such mastery of the material that it soon becomes clear that one is in authoritative hands, and topics are selected and developed only to a point where they prove adequate for future needs.' The Times Higher Education Supplement

Praise for the first edition: '... ought to inspire more physicists and astronomers to teach and learn the other half of the twentieth century's revolution in physics.' Foundations of Physics

Praise for the first edition: 'The book is a goldmine of cleverly constructed problems and exercises (and solutions!).' Nature

Praise for the first edition: '... provides the first step into general relativity for undergraduate students with a minimal background in mathematics.' Zentralblatt MATH

'Several generations of students have benefitted from the first two editions of Professor Bernard Schutz' beautiful introductory textbook on tensor algebra, manifolds, physics in curved space times, and Einstein's field equations. Why another edition now? The answer is that, in the last years, precision measurements of stellar orbits around the central massive black hole in the Galactic Center, the detection of gravitational waves from in-spiraling binary black holes and neutron stars with LIGO, and the detection of the central 'radio wave shadow' of the supermassive black hole in the galaxy M87 have suddenly opened the magical w...

Bernard Schutz is a Professor in the School of Physics and Astronomy at Cardiff University, Wales, and Director (ret.) at the Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Germany. In 2019 he was elected a member of the US National Academy of Sciences, and in 2021, he was elected a fellow of the Royal Society, in recognition of his seminal contributions to relativistic astrophysics.

Preface to the third edition page; Preface to the second edition; Preface to the first edition; 1. Special relativity; 2. Vector analysis in special relativity; 3. Tensor analysis in special relativity; 4. Perfect fluids in special relativity; 5. Preface to curvature; 6. Curved manifolds; 7. Physics in a curved spacetime; 8. The Einstein field equations; 9. Fundamentals of Gravitational Radiation; 10. Spherical solutions for stars; 11. Schwarzschild geometry and black holes; 12. Gravitational wave astronomy; 13. Cosmology; Appendix A. Summary of linear algebra; References; Index.