The Geometry of Spacetime: An Introduction to Special and General Relativity (Undergraduate Texts in Mathematics) 1st Edition by James J. Callahan (PDF)

Description

Hermann Minkowski recast special relativity as essentially a new geometric structure for spacetime. This book looks at the ideas of both Einstein and Minkowski, and then introduces the theory of frames, surfaces and intrinsic geometry, developing the main implications of Einstein’s general relativity theory.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I have spent a ton of money over the years trying to buy a book that I could learn relativity from. This is it. Although I have only worked my way through the first 3 chapters at this point, these three chapters are worth the price of the book. The subject is presented in a geometrical fashion, and up until the end of chapter 3, I have not been buried in an avalanche of subscripts. Having glanced at later chapters, I know that the subscripts and superscripts are coming, but I also believe that I will be prepared for them when they arrive.Well done./***/Added in May 2004I have now taught quite a few readings from this book and will be teaching a course from it this summer. It is wonderful.

⭐This book gets at the essential core ideas of the topic and expresses them in as clear and accessible a manner as anyone could given the inherent difficulty of the subject matter.

⭐Great introduction to Special and General Theory of Relativity for those who are still developing their mathematical maturity on the subject.

⭐This book is great for teaching the math behind GR using excellent examples from Math and Physics problems (for another great problem solver see also Schaum’s Outline of Tensor Calculus, but this has less Physics). It is a bit long winded, spending alot of time on SR and in some place just over the top (for Physicists!), but once through it there should be no problem going to the more advanced texts which deal with more of the uses of GR. At the same level I would also recommend Schutz’s First Course in GR, however, Callahan’s book goes through and explains the use of the math better, whereas Schutz’s is better for uses in GR, surprisingly this is the strength of Callahan’s book: you can’t really do the Physics properly unless you can do the math! After this it’s on to more Physics orientated books like Carroll’s excellent Introduction to GR, as a stepping stone to MTW’s Gravitation and Wald’s GR.

⭐This book is a terasure in its own right !everything is explained using diagrams, figures with simplicity and rigor.you will never feel you got lost anywhere. Although the introduction to tensors is limited, the application of Fermi coordinates is great although I would have expected to see the actual derivation of vacuum equations as einstein first wrote it .The proofs are excellent. The application, though limited but clearly exposed.

⭐I have not had a chance to work through the whole book yet, but I think the previous reviewer is correct – it is an excellent book. I particularly like the approach in the early chapters where special relativity is treated with the basic linear algebra of linear transformations. This gives several interesting applications that students often don’t see early in their mathematical career.The later chapters cover the geometry of surfaces and general relativity. I would like to learn GR in a “coordinate-free” fashion, but Callahan does not take that approach (and gives his reasons clearly in the introduction). In scanning over the later chapters it looks like the coordinate approach is balanced with lots of physical and geometric explanation.

⭐After long reflection, I am convinced that this book is the most finely crafted piece of teaching I have ever encountered. If you have hard interest in relativity, spacetime, cosmology, but lack facility with mathematics more advanced than calculus and linear algebra, Callahan will lead you into a deeper understanding of the mathematics than you would have believed possible.

⭐I’ve only read the first third in detail, but so far this book is frankly disappointing. The treatment is lightweight and padded out with verbiage, some of it oddly off-key. What math or physics student at this level needs (for example) an elementary account of the properties of hyperbolic functions? Spacetime diagrams are drawn with the time axis horizontal, which is something I’ve never seen in any other relativity text. Okay, it’s a minor point, but I found this and similar nonstandard usages a constant irritant. More seriously, the development of relativistic momentum and covariance in chap.3 is quite incoherent, and the definition of 4-velocity is WRONG (at least, by everyone else’s standards – it isn’t even a 4-vector). There are plenty of exercises, which is good, but no solutions at all – not even outlines – which is not so good.The book takes over three hundred pages to get to general relativity (where there seems to be no mention of the equivalence principle!), and I doubt if it’s worth the effort. You would do better to work through Foster & Nightingale’s ‘Short Course in General Relativity’, which is a first-rate and accessible introduction if you have a little background in special relativity. And it’s two-thirds the price.Conclusion: There may be a good book waiting to be written on these lines, but I’m sorry to say this isn’t it. I wouldn’t recommend it to anyone as a first course in relativity.

⭐* PhysicalThis book – in my hardback edition anyway – is very sturdily bound. The paper is of good quality matt and not the glossy kind.* Target Audience, A – level / H.N.D, undergraduate, graduate?The book is aimed at undergraduate math level, perhaps second year and above.* What is the explanation to this topic like then?This book runs on the healthy exploration and explanation of the Mathematics of these General and Special Relativity theories, and leaves the bulk of the physical interpretation of these theories to other books. The author manages a marvelous clarity to the maths. There are many formulae and how to apply them. It’s a beautiful book that’s hands – on. You need knowledge of matrices, hyperbolic geometry formulae, vector calculus, lorentz transformation techniques, 3d calculus, limits, mappings from differing geometries such as euclidean and spherical geometries. newtonian gravitation concepts. too. This book allows jumping from topic to topic, chapter – to – chapter that some books block as required. Generally, It assumes less than some books, and rolls it sleeves – up to help explanations of these topics as required.* Best bits (subjectively)The best bits in this book is its author allow a true revelation in the manner in which the subject of Tensors is explained. I realise now that this book is the ‘real deal’ to learn comprehending real Math of how to apply and comprehend this vital shorthand for Einsteinian tensor techniques. I thought i grasped this already, but this books explanation is a revelation! Starting from page 307 is a real help to grasp to its introductory Tensor usage. Although i am not sure if it’s also been boosted from previous readings from other books which may have helped too? Where i ground to a full stop is the in depth explanation in page 349 proved too complex at this time for me! I could make some more progress after this but it starts to become requiring more in depth studies to crack this.* SummaryThis book makes you feel that your reading real mathematical topics and it’s a lovely self – contained study course. I really enjoyed this book and will continue to reread this book. I have been reading this book since Dec 2015 and need to boost my knowledge after this date of writing this review. As before, if you’re stuck, use your browser to go to a well – known video sharing website and enter in it’s search engine, ‘Tensors’ and it’s also a boost to aid comprehension.

⭐Ce livre de la série “Undergraduate Texts In Mathematics” est une excélente introduction à la relativité. Comme l’indique son titre, l’auteur y présente graduelement la structure géométrique de l’espace-temps dans le cadre de la relativité restreinte puis générale. L’aspect mathématique y est bien sûr extrêment bien introduit mais sans oublié l’aspect physique. Le niveau mathématique d’entrée y est raisonnable : algèbre linéaire et analyse. A bien y réfléchir il s’agit probablement de l’un des livres par où j’aurais du commencer – tant se forger une image et une intuition géométrique peut aider par la suite.

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