Spacetime and Geometry: An Introduction to General Relativity

by Sean Carroll

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.

Genres: Physics, Science, Textbooks, Nonfiction, Mathematics, Reference, Technical

750 pages, Hardcover

First published September 28, 2003

About the author

Sean Carroll is a physicist and philosopher at Johns Hopkins University. He received his Ph.D. from Harvard in 1993. His research focuses on spacetime, quantum mechanics, complexity, and emergence. His book The Particle at the End of the Universe won the prestigious Winton Prize for Science Books in 2013. Carroll lives in Baltimore with his wife, writer Jennifer Ouellette.

Reviews

[Chris · Rating 5 out of 5]

I worked through most of this book (except two appendices and the last two chapters) as part of an independent study for school and I can honestly say that it is, bar none, the most well written textbook that I have ever read.

If you have a solid mathematics background (basically the first 5 chapters of Schutz' A First Course in General Relativity, the sections on tensors are a little too brief for seeing this stuff the first time) there is absolutely nothing better.

I do have a few complaints, though. I really would have liked to see some more worked examples, especially in chapters 2 and 3. There is a lot of fairly advanced mathematical machinery being developed, and a simple example would have illuminated the discussion a lot more. In particular, the section on differential forms was hard to follow (I'm still not sure that I understand what a Hodge dual is, even after many readings!)

Oddly enough, I found the section on causality to be the most difficult to understand in the whole book and there is almost no math in it! I think it could really use a rewrite, as it is nothing more than a long list of definitions with very little motivation.

Minor shortcomings aside, I have literally never learned so much from any other book. It's that well written!

[Alan Chan · Rating 4 out of 5]

I skipped all my General Relativity classes to read the book and got A+. Totally worth it.

[Stany · Rating 5 out of 5]

The challenge with writing a book on GR is always in finding the right balance between mathematical rigor and niceties on the one hand and physics “hand waiving” arguments and interpretations on the other hand. Mr Carroll has found the right balance throughout the book.
The result is an excellent introduction to GR for advanced undergraduate and starting graduates students of theoretical physics. For those more inclined to mathematical formalism, Wald remains the reference.

[Henrique Legoinha · Rating 5 out of 5]

This book is straight to the point without sacrificing any physics’ discussion.
Very insightful!

[Angela Powell · Rating 4 out of 5]

While reading this book I was remembering my school days. That time I was excited about general relativity and the history of time but I did not have any good book to read on the subject. Now I can say this is a very good book to begin with the concept of space and time.

The relation between geometry and physics has a long tradition. The fusion of geometry and physics is a strong stimuli for modern science. Although, the combination of geometrical field theory with quantum mechanics is a bigger challenge for us. Similarly, geometric and thermodynamic properties and its connection with the primordial universe need further studies. Overall the book is interesting to start with.

[Simon Mcleish · Rating 3 out of 5]

This is a pretty good textbook on the mathematical physics underlying the theory of general relativity. Despite a consistent attempt to explain the significance of each idea, there are large numbers of new concepts, and of notation conventions and shortcuts, which make it harder to read (for someone like myself whose background is pure mathematics rather than physics) than it otherwise could be. Deserves to be read with more thoroughness than I had time to give it - taking notes while reading would have certainly made it easier to follow.

[Richard Marney · Rating 5 out of 5]

A pre-course reading of selected chapters. I think (hope) I have picked up enough not to get lost during the term! As I fully expect that I will, I am relieved I can turn bright red remotely 😱.

[Jaime Montoya · Rating 4 out of 5]

This book is a great journey to understand the classical general relativity theory, a beautiful theory about the nature of space-time. Through tough experiments the author explains in a masterful way how the original hteory was created by Einstein and others. Right from the beginning, the author introduce the reader into theQuantum Mechanics and the flavor of a potential Quantum Gravity Theory, therefore we have a very powerful introduction to the Quantum Mechanics , starting from the classical and exploring some beautiful concepts about the unification. There is a big effort the reader should made to complete the amazing journy, because the author dives deeply into the mathematical background of the theory as should be and as I expected, but is an effort worth to do.

[Francesca Fernandes · Rating 5 out of 5]

ok so i haven't actually finished this textbook, but in the 3 chapters I did get through this/last quarter, it did give me many, many, many tears and many, many, many headaches and existential crises. perhaps that is because it is a bit out of my range too, but its explanation of differential forms & tensors & metrics did make me want to jump into a hole and die sometimes. (and the reason i don't think it's entirely my own fault/my own "stupidity" is because i found another resource on differential forms and i worked through the entire 60 pages and understood it all ... so i'm rly blaming Carroll over here.)

[Heather · Rating 2 out of 5]

I think the cover used to be grey. Either that or I just associated it with grey dark times of confusion. It could have been the prof being too smart (or confused) to teach the concepts but this book did not add any clarity. Also tensors are just not fun.

[Jiachen Guo · Rating 5 out of 5]

This is not an introductory book in my opinion. It should be supplemented with other GR books like Hobson, Ta-Pei Cheng & Zee. I also find Schutz's "Geometrical methods of mathematical physics" particularly useful for understanding the differential geometry section in Carroll.

[Bjørn Remseth · Rating 4 out of 5]

I haven't read this book through in detail, yet I've been reading in it it on and off for a number of years now so I guess that qualifies me to have an opinion about it :-) I do intend to grok the entire book to some extent, some day, but this material takes time and space to interact with, and that can be hard to find in a busy schedule. It's not that GR is is intrinsically difficult. Carrol's explanations are excellent. The concepts are clearly explained and mostly easily understood, when they are read. But they are complex. There are many "moving parts" in tensors, and an ability to use them as tools when solving problems is not something that comes for free. For good textbooks on complex topics, and this is a good textbook, it is always somewhat frustrating to first believe that one grasps a concept while reading about it, only to find that the understanding doesn't translate particularly easily to an ability to solve problems. As an example: It's not that hard to understand in principle how Christoffel symbols are used to "patch up" derivatives of tensors to form covariant derivatives that transform as tensors, but it's a bit more work to actually use them when patching up whatever metric one needs to work in when solving problems.

In his blog Sean Carroll suggests to take a look at https://www.amazon.com/Problem-Book-R..., and that seems like a good recommendation. Finding space an time for it is still an issue, but may be worth the effort :-)

Anyway. This book has been, and still is an inspiration. It led me to start digging into geometric algebra which is _such_ an interesting structure. It's so strange that I managed to get through undergraduate and graduate school in computer science without learning about it, but it's never too late, and I'm happily absorbing it now.

[Michael Wu · Rating 4 out of 5]

Only read the first 5/9 chapters (first 4 are the core text) and skimmed some of the math. That being said, very well written. Carroll's voice is that of a mathematician - a bias towards theory and e.g. being careful when abuses of notation occur, which I appreciated.

One critique is the tendency toward an "inline" style (text in paragraphs) over a "block" style (definition, theorem, main takeaways boxes) making it harder to "find the upshot", particularly in some of the longer calculations, though this critique can be given to most 20th century math texts.

Read this mainly out of curiosity. It seems a satisfactory enough text that if I ever decide to learn more (not sure why I would, but never know) I'll probably return here for a more thorough read.

[Thomas Atwood · Rating 5 out of 5]

For physicists only. I have read MTW and much of Weinberg, but Carroll is the clearest and most up-to-date textbook on General Relativity I've seen so far. I enjoyed reading it and it will become my primary GR reference. My goal was to get more familiar with GR, particularly the latest practice, not to become an expert, so I didn't bother to work any of the problems. My main take-away from it was that it seems that the Einstein equations are so hard to solve that most of the applications have been in the weak field limit. As it happens, my interest in GR is in the strong field limit, so Carroll (and anybody else) may not be much help there. Nevertheless, this is a very friendly encapsulation of General Relativity.

[Joshua Zeidner · Rating 3 out of 5]

I recently read the first chapter. Carroll is a talented writer that much is clear(although I understand his wife plays the role of editor). There are many instances of colorful yet entirely appropriate phrasing that are rarely found in physics texts. This adds to the entertainment aspect.

I found the first chapter less than inspiring. Seems to want to concentrate on secondary ideas such as Dual Vectors where they don't seem appropriate at that level. Relativity is a complex subject and there is no right way to teach it, so I respect Carrols contribution. I can't really think of any other text I might recommend for someone who wants to understand GR.

[Nazir · Rating 4 out of 5]

I worked through most of this book for my graduate general relativity class. It should be a nice tie-in to something like Gravity by Hartle or Covariant Physics by Emam. However, the book is challenging at times. Particularly in the beginning where all of the differential geometry is being developed (the discussion on forms was particularly grueling). But the book is a great place to learn relativity from. It is very complete, and Sean Carroll balances physical intuition and rigor very well. The curvature and black hole chapters were simply phenomenal. So I’d definitely recommend this book is if this is your second rodeo with general relativity.

[Sean McLaughlin · Rating 5 out of 5]

Great textbook I refer to regularly

[Chandra Prakash · Rating 5 out of 5]

Best book to start, but you gotta learn maths first, it does skip a few steps in the derivation, but that's not a big deal to figure out.

[Jason · Rating 5 out of 5]

Spacetime has pretty math associated with it.

[Athul Muralidhar · Rating 5 out of 5]

This is one amazing book on general relativity

[Adrian Sanchez-Reyes Febrian · Rating 5 out of 5]

This book, and ONLY this book, helped me pass my General Relativity 3rd year subject at university. I knew this book by heart, and I loved every part of it.

[Yuri · Rating 5 out of 5]

Amazing introduction to the theory of General Relativity. Great explanations, although I would have preferred a more precise mathematical formulation. Still a great book!

[Sanar Othman · Rating 4 out of 5]

But how do you finish reading a textbook anyway?

[MARC L'ESPERANCE · Rating 4 out of 5]

VPR source, Interesting idea to approach physics first through Quantum, and it's wave function.

[Lila]

So helpful for thesis!

[Piet Bracke]

For those with advanced knowledge of mathematics.

[Daniel · Rating 5 out of 5]

Probably one of the best book for anyone that wants to ease into the subject of relativity! Sean Carroll is brilliant as always.

[Kristof · Rating 4 out of 5]

If you want a good introduction on general relativity, read this book! It is very clear but also has enough emphasis on the mathematical aspects of the theory, the balance between physical and mathematical aspects is very well done here.

[Astrila · Rating 2 out of 5]

This book stinks. Not funny at all (which is a requisite for physics textbooks), very non-imaginative. There must be better GR books out there.

[Nick Black · Rating 4 out of 5]

An exquisite book.