Spacetime and Geometry: An Introduction to General Relativity

It's a high quality book that makes you enjoy reading it. The author is an expert no doubt. The subject is deep but Dr Sean makes it possible to follow a very good portion of the book even with no prior knowledge or experience in the subject at all.

Content: author's style of rambling and prematurely tossing out equations and comments ("don't worry - you won't understand this now") is irritating. The tone is conversational in a negative way, constantly digressing without the necessary supporting definitions or development.Very first equation about Lorentz transformations (1.23) is nonsense. Carroll has it correctly in his online notes; how did this garbled equation creep into the printed edition?Personal peeve: The metric {-1,1,1,1} is awkward, resulting in proper time d𝜏^2 = -ds^2. Other (better) books use {1,-1,-1,-1}.Printing: awful. Looks like a blurry photocopy. Also, the printing is off-set, so that the right edge of the printing is about 0.5 cm from the page edge, while there is a giant left margin. (This is the same for all pages.)With so many excellent texts -- Wald, Schutz (new 3rd ed.), D'Inverno (new 2nd ed.), Ohanian & Ruffini, Padmanabhan, Zee, & the timeless Dirac, Weinberg, MTW -- Carroll's book adds nothing new.

This is an outstanding textbook on general relativity. It's very detailed, well written and the order of the topics is very well chosen, covering a wide range of themes. The level is appropriate to graduate student, with a quite decent mathematical background.In particular, the first chapter is a review of special relativity: a brief but clear summary, useful to become familiar with the use of the 4-vector notation, too. The second and third chapters are committed to manifolds and curvature, and you have to learn the fundaments of differential geometry. The chapters from fourth to seventh are focused on the "real" general relativity, from Einstein's equation to gravitational waves: this is a quite advanced dissertation, and I think it is necessary to have a basic background from an introductory book. The last two chapters are an introduction to cosmology (brief, but pretty good) and an introduction to quantum field theory in curved spacetime (but I never read this chapter, sorry!).Remark that the book contains ten (10!) very useful appendixes on additional topics that are not debated in the ordinary chapters: they are a good extension to examine in depth some themes (in particular on a second reading).Very good binding and hardcover: it's durable and solid, with a good value for money.

Last year, when I was at my Dad’s and stepmom’s house, I found the book “An Introduction to General Relativity, Spacetime and Geometry”, by Sean M Carroll. I was struck by the promise at the beginning of the preface: “.. it is an unalloyed joy to finally reach the point in one’s studies where these phenomena may be understood in a rigorous quantitative level. If you are contemplating reading this book, that point is here.” For me the book has lived up to this promise. I have been reading the book off and on since then and working some of the problems. I studied general relativity a little in college several decades ago, but there were many vague ideas floating in my head. This book has sharpened up the concepts, explained new ones, and connected them in a good way.

Very clear explanations of the beautiful geometric basis of General relativity. particularly the tratment of curvature, geodesics and the Schwarzschild metric in chapter 5.

This is one of the best books on general relativity. In my opinion it is somewhere between the classic Misner, Thorne, and Wheeler tome and Wald's General Relativity in its mathematical requirements. I like the tone of the discussion of topics. It is comprehensive enough to be useful in applications and leading to more advanced studies.

Shipping is taking a bit long to deliver but once I got it im pleased with the quality.

I purchased this book in 2004 finally got around to reading and doing the exercises this year ( such is the life of a professional poker player). I purchased the book as a review having already gone through MTW decades earlier but I was pleasantly surprised by the treatment of modern topics like the alternative theories and relation to string theory and QFT in curved space time. The math is excellent and my only objection to the book is that the errata page is not up to date - I have found the usuall amount of errors in any advanced physics book. This is a great graduate level introduction - not a reference work.

This book asks a great deal of the reader. The material on tensors is very short and if you are not already familiar with them you will struggle. Likewise the section on one forms & dual vectors. My head was spinning after reading the material on them. Each page contains so many ideas, new material that I needed to read everything about 10 times before I could move on. In summary I found this book difficult, but then it is a difficult subject. It covers a very wide range and is certainly a comprehensive introduction to the subject. For the expert reader I think. For myself I will persevere as the book has so much of value.

Worth and interesting concepts

Was mir als Mathematiker besonders auffällt ist, dass Carroll zwar mit der Brille des Physikers schreibt, aber offenbar über ein profundes mathematisches Hintergrundwissen in Sachen Tensorrechnung, Riemannschen und Semi-Riemannschen Mannigfaltigkeiten verfügt, was man an vielen Stellen im Buch feststellt. Das Werk ist - im Unterschied zu vielen anderen Standardwerken - flüssig zu lesen. Die Anhänge sind äußerst interessant. Dem Mathematiker sind ergänzend John M. Lee "Riemannian Manifolds" und Barrett O'Neill "Semi-Riemannian Geometry - with Applications in Relativity" zu empfehlen.

Ho letto solo il primo capitolo e quindi questa recensione è sicuramente prematura. La prima impressione è che il testo sia completo e approfondito, sia dal punto di vista dell'interpretazione fisica sia da quello della formulazione matematico-geometrica. Il livello di complessità matematica è molto alto. Sono un lettore dilettante della fisica e il primo capitolo (relatività ristretta e teoria classica dei campi) sarebbe stato fuori della mia portata se non avessi già fatto delle letture sul tema (in particolare il Theoretical Minimum di Susskind). Vero è che questo capitolo, dichiara l'autore, è una rapida review di materia che si suppone già nota. Spero che i successivi adottino un approccio più didascalico.

I've read Ta-Pei Cheng, the first few chapters of Lasenby, Efstathiou & Hobson and Loring Tu's Manifold book before reading this book. I can imagine that the Carroll's chapter on differential geometry will completely baffle any physics student that have not been exposed to manifolds before. But otherwise this book is has very good content and exercises.