Customer Reviews

The Geometry of Spacetime

5 star:		(7)
4 star:		(3)
3 star:		(0)
2 star:		(1)
1 star:		(0)

 

 

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.

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 is one of the best introduction to General Relativity. It is the most accessible introduction to differential geometry. Naturally you have to know calculus, linear algebra, and the basics of special relativity. I bought many books on the subject, and this one belengs to the set I suggest for self-learning.

This is an excellent introduction to General Relativity. As far as I have seen, this is the most accessible introduction to the subject. Any undergraduate who has had calculus, linear algebra, and knows the basics of special relativity will do fine with this book. I may be "picky" in not giving this a five star rating, but there were some portions of chapters 6 and 7 that were hard to follow. I should mention however, that I have been unable to find a text that does explain such material any better, while remaining accessible to undergraduates.

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.

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.

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.
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Added in May 2004

I have now taught quite a few readings from this book and will be teaching a course from it this summer. It is wonderful.

We all get an initial taste of relativity in Freshman/Sophomore physics. But where to go next can be a problem. If you like the math accompanying your physics a bit more rigorous than "hand waving", this is a great book. I tried Schutz's book but didn't find the math self contained or rigorous, while trying to jump into Wald's graduate level text on General relativity was way too much to soon. This book strikes a good balance between the physics and the math. Nice coverage of the Lorentz transformation and the invariance of Maxwell's equations under it. Minkowski space time and "hyperbolic" geometry (nice review of hyperbolic functions in analogy with trigonometric functions). And a self contained introduction to differential geometry (as applied to general relativity). I'm finding this great for self study.

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.

At times this book can be confusing, often the author will make something unclear by leaving out a simple sentence or two. I can't really compare it to other texts- although i've looked through many this is the first I tried to actually learn from, but as far as a textbook goes it's not the greatest. In many places once you figure what he's trying to say, you also realize that an added sentence or step or justification would've made it far easier to understand.