Review of An Introduction to Spacetime and Geometry by Sean M. Carroll

Phillip Helbig

The Observatory, 140, 1274, 33–35 (February 2020)


This is a book review of An Introduction to Spacetime and Geometry by Sean M. Carroll. There is no shortage of books on general relativity, even at the same level of presentation as this one. So why another book? Carroll notes that many of the well known books on GR emphasize their own viewpoints, which are seen by some as idiosyncratic; this book offers a `neutral' approach and also concentrates on the basics of learning GR---applications are discussed, but not extensively, and even there the emphasis is on learning GR. The first three chapters cover special relativity and differential geometry, before gravitation is introduced in chapter four. The next four chapters are on applications, including such astronomical topics as black holes and gravitational radiation, though the emphasis here, like elsewhere, is on mathematical formalism and not astrophysical processes. Thus, the book's title is very descriptive, and the presentation follows the traditional pattern in GR books, introducing differential geometry and tensor calculus before moving on to physics, though the discussion of special relativity at the beginning whets the appetite. The chapter on cosmology is perhaps the closest to more-astronomical accounts of the topic. The final chapter, on quantum field theory in curved spacetime (necessary to understand Hawking radiation, for example), is unusual in an introductory text. I recommend the book for those who know little about GR but want to learn more; it is a useful bridge between more-qualitative or even popular introductions and more-advanced textbooks.


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