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*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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