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Spacetime and Geometry: An Introduction to General Relativity

26 customer reviews
ISBN-13: 978-0805387322
ISBN-10: 0805387323
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Editorial Reviews

From the Back Cover

Spacetime and Geometry: An Introduction to General Relativity provides a lucid and thoroughly modern introduction to general relativity. With an accessible and lively writing style, it introduces modern techniques to what can often be a formal and intimidating subject. Readers are led from the physics of flat spacetime (special relativity), through the intricacies of differential geometry and Einstein's equations, and on to exciting applications such as black holes, gravitational radiation, and cosmology. For advanced undergraduates and graduate students, or anyone interested in astronomy, cosmology, physics, or general relativity.

About the Author

Sean Carroll is an assistant professor in the Physics Department, Enrico Fermi Institute, and Center for Cosmological Physics at the University of Chicago. His research ranges over a number of topics in theoretical physics, focusing on cosmology, field theory, and gravitation. He received his Ph.D. from Harvard in 1993, and spent time as a postdoctoral researcher at the Center for Theoretical Physics at MIT and the Institute for Theoretical Physics at the University of California, Santa Barbara. He has been awarded fellowships from the Sloan and Packard foundations, as well as the MIT Graduate Student Council Teaching Award. For more information, see his Web site at


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Product Details

  • Hardcover: 513 pages
  • Publisher: Addison-Wesley (September 28, 2003)
  • Language: English
  • ISBN-10: 0805387323
  • ISBN-13: 978-0805387322
  • Product Dimensions: 7.5 x 1.2 x 9.1 inches
  • Shipping Weight: 2.4 pounds (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (26 customer reviews)
  • Amazon Best Sellers Rank: #255,117 in Books (See Top 100 in Books)

More About the Author

Sean Carroll is a theoretical physicist at the California Institute of Technology. His research focuses on fundamental issues in quantum mechanics, gravitation, statistical mechanics, and cosmology. He has wide-ranging interests, including in philosophy, complexity theory, and information.

Carroll is an active science communicator, and has been blogging regularly since 2004. His textbook "Spacetime and Geometry" has been adopted by a number of universities for their graduate courses in general relativity. He is a frequent public speaker, and has appeared on TV shows such as The Colbert Report and Through The Wormhole with Morgan Freeman. He has produced a set of lectures for The Teaching Company on dark matter and dark energy, and another on the nature of time. He has served as a science consultant for films such as Thor and TRON: Legacy, as well as for TV shows such as Fringe and Bones.

His 2010 popular book, "From Eternity to Here," explained the arrow of time and connected it with the origin of our universe. "The Particle at the End of the Universe," about the Large Hadron Collider and the quest to discover the Higgs boson, was released November 2012. "The Big Picture: On the Origins of Life, Meaning, and the Universe Itself" will appear in May 2016.

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Customer Reviews

Most Helpful Customer Reviews

279 of 296 people found the following review helpful By Mitchell Chan on December 14, 2005
Format: Hardcover
My comments come with a few caveats.

1. This is my fourth GR book.

2. I'm not hardcore into physics. I'm not a physic grad and I'm reading GR for fun. I have a decent graduate math background but I've been corrupted with 10+ years in working in various roles software engineering, electronics engineering and marketing.

3. I assume that since you're considering buying this book, you're goal is to get at the "real" GR, not the watered down discover channel version.

With these caveats in mind, here are my comments.

First, on a scale of 1-5, I rank Carroll at level 3 in terms of math/physics maturity and thoroughness. Here is my full ranking of authors from my limited reading: 1. schutz 2. hartle 3. penrose 3. carroll 4. wald 5. physics journal articles

Second, using the rankings above, I recommend Carroll as the second port of entry. If you're comfortable with multivariable calculus, start with schutz (#1). You'll get warm fuzzies doing the toy exercises. But Schutz is tensor/math-lite. If you've had advanced calculus and geometry already, jump in with carroll (#3). But you'll be hard-pressed to find anyone else as polite to the reader. He won't prepare you for 80 percent of what's published. If you're ready to throw off the training wheels and jump dive into mainstream GR go with Wald (#4).

Note that Hartle (#2) is a good "tweener" book with feel-good exercises and some of the full-on GR equations at the end. I bet most instructors teaching a first year grad course would go with Hartle along with a dose of supplementary material.

Third, don't expect Carroll to be your last GR book purchase if you want to reach the promised land (see caveat #4). Living and breathing GR is found in physics journals and for that you'll need Wald or another advanced GR book.
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130 of 135 people found the following review helpful By smallphi on March 7, 2005
Format: Hardcover
I had a course based on that book and I've read chapters 1-6 (out of 9 chapters total) plus all the appendices. Also, I've solved some of the problems.

The math chapters 2 and 3 will teach you tensor analysis on manifolds in much clearer way than other books. The book makes a clear distinction between assumptions, choices (like working with a metric compatible connection), or derived facts. It also makes a difference between a Christoffel connection and a generic connection. The appendices will give you a feeling for some new to you math on manifolds like pullbacks, Lie Derivatives, hypersurfaces etc.

Chapter 4 is worth reading too cause it makes clear that Einstein's equations are just the simplest guess out of many other possibilities. It shows how we generalize physical laws from special relativity to GR making it clear our choices are the simplest ones but not the only ones possible.

The chapters after that discuss applications of GR like black holes, gravitational radiation, cosmology etc. Of these, I've read only the black holes chapters 5 and 6 and I wasn't able to understand 100% what was goin on. The problem was that the book uses concepts that you still don't quite understand if you are a beginner like 'spacelike singularity' or 'conformal diagrams'. That is informative but the book doesn't provide the necessary level of detail and examples for beginners so you could really master such concepts and use them in your practice.

There are problems after each chapter but not the necessary beginners problems that increase your conceptual understanding of the theory. Instead, some are just tedious algebra of type 'find the curvature for some general form of the metric' for which specialists in the field use symbolic programs like Mathematica.
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85 of 96 people found the following review helpful By Amazon Customer on February 17, 2004
Format: Hardcover
This book has helped me long before it was ever published! It is based off of lecture notes that Carroll gave for a graduate level General Relativity course. These notes are still freely available at:
But you miss out on extras like better diagrams, more examples and exercises, so this is still a great buy!
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47 of 52 people found the following review helpful By A Customer on March 17, 2004
Format: Hardcover
I may be biased (as a student there), but the University of Chicago has the market for textbooks on GR cornered. Between Sean Carroll and Bob Wald, the student has everything he needs. I do have to reccomend reading this one first though, as the explanations are more physical (where Wald is more formal) and the style is more readable and easier to digest. In short it is probably the best book on the market from which to learn GR. Once you finish this book, add Wald's to your library for a more complete reference set (Wald's book is likely the best on the market once you already know GR).
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31 of 34 people found the following review helpful By Dr. Joseph R. DELLAQUILA on October 24, 2004
Format: Hardcover
In my graduate studies in physics, I had never taken a course in general relativity or differential geometry. Carroll's book is the right place to start. It is very clearly written and it has a wealth of diagrams to help when the discussion tends to get somewhat abstract. I found it enlightening, entertaining, at times deep and always worth the effort. The material on differential geometry and the appendices are examples of textbook writing at its best. If you have the proper background, go here before attempting Wald's General Relativity or any other more advanced treatise. Joseph R. Dell'Aquila, PhD
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