A First Course in General Relativity

Clarity, readability, and rigor combine in the third edition of this widely used textbook to provide the first step into general relativity for advanced undergraduates with a minimal background in mathematics. Topics within relativity that fascinate astrophysics researchers and students alike are covered with Schutz's characteristic ease and authority, from black holes to relativistic objects, from pulsars to the study of the Universe as a whole. This third edition contains discoveries by astronomers that require general relativity for their explanation; two chapters on gravitational waves, including direct detections of gravitational waves and their observations' impact on cosmological measurements; new information on black holes and neutron stars; and greater insight into the expansion of the Universe. Over 300 exercises, many new to this edition, give students the confidence to work with general relativity and the necessary mathematics, while the informal writing style and worked examples make the subject matter easily accessible.

Table of Contents:
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.

About the Author :
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.

Review :
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 world of strongly curved spacetime to precision experimental tests. These experiments and much more to come from ground- and space-based gravitational wave studies have started a renaissance of interest in Einstein's theory.' Reinhard Genzel, Max Planck Institute for Extraterrestrial Physics 'Students and teachers of general relativity will welcome this new edition of Schutz' hugely popular text, significantly broadened to cover the astonishing discoveries of gravitational-wave astronomy and their implications. A pioneer of the geometrical approach to undergraduate-level teaching of GR, the book remains unmatched in its highly readable style. With vim and authority, Schutz leads his readers masterfully from mathematical foundations to the forefront of research in astronomy and cosmology, providing them with the tools to understand future discoveries. With this new edition, Schutz' classic text remains as fresh and relevant as ever.' Leor Barack, University of Southampton 'An outstanding textbook on general relativity written with the author's customary clarity and in his engaging style. It includes not only the basics of general relativity, but also recent developments in the direct detection of gravitational waves. A clear exposition of the essential ideas and methods.' Rong-Gen Cai, Chinese Academy of Sciences 'Professor Schutz' informal style bewitches the reader into absorbing profound and complex concepts effortlessly. Physics is explained in a lucid style with minimal mathematics, without compromising on rigour. The recent excitement in the field of gravitational waves and its implications for astronomy and cosmology is adeptly conveyed. This edition has been enriched with several more exercises which the student or the young researcher will find illuminating and instructive.' Sanjeev Dhurandhar, Inter University Centre for Astronomy and Astrophysics 'When I first taught from this book in the 1980s, my students and I loved it for its unusual combination of clarity and brevity. This third edition is not quite as brief because so much has happened in the subject! But for an all-around text with clear writing and an engaging style, it is still top of the class.' Clifford Will, University of Florida 'A First Course in General Relativity by Bernard Schutz is an outstanding introductory text on Einstein's theory of general relativity and offers an invaluable resource for students interested in understanding the formal and physical foundations of modern spacetime theory.' Karim Thebault, University of Bristol 'As with its previous editions, this textbook provides a fantastically accessible introduction to the key physical concepts of general relativity and the formalism used by its practitioners. The third edition gives a much-needed update accounting for discoveries since the previous edition, with the chapters on gravitational waves in particular serving as outstanding tutorials for students who are interested in astronomical applications of this subject.' Scott Hughes, Massachusetts Institute of Technology