|
|
Title: Spacetime and Geometry: An Introduction to General Relativity
Purchase
Item
Manufacturer: Benjamin Cummings
List Price: $109.33
Our Price: $80.60
|
|
| Customer Reviews: |
| Spacetime and Geometry: An Introduction to General Relativity by Benjamin Cummings Wordy and Wonderful | This is an advanced text, but all the same it is not particularly rigorous or dense, so it is in principle accessible to the beginner. With an easy authority, Carroll leads us on a wandering journey through the mystical lands of general relativity. This is very different from, and compliments nicely, the clarity and directness of Wald. As a student of GR, I use Wald for the bottom line on any subject, and Carroll for the random physical or computational insights that I invariably find in any section of the book. Carroll's prose is like music to the ear and I always enjoy myself when I decide to open up this book.
Be warned that there are lots of mistakes in this first edition--you might want to wait for the second one.
Also, his chapter on cosmology is better than any I've seen. | | Spacetime and Geometry: An Introduction to General Relativity by Benjamin Cummings BY FAR the best book on GR | I am currently on the 4th chapter of Carroll's "Spacetime and Geometry" and thus far I am amazed at how clear it is. Sure there is a lot of math in it however that also is very clearly explained. In fact, I think that Carroll explains the differential geometry material better than any mathematician has in any book on the subject. If you want to learn general relativity, there is no getting around the math; sooner or later you'll have to learn it. I'd suggest, especially if you are self-studying the subject, to rather pick up this book and go through it than pick up a more "elementary" text and a book on Riemannian geometry to look at later.
(Although I do also highly recommend Kay's (Schaum outline) "Tensor Calculus" for self study. The prima donnas don't like Kay's book because it "doesn't have enough theory." I suppose if a freshman calculus book does not have the Lebesgue integral defined in ti they'll complain about that too.)
Because, you can always skip through certain sections if the math is too heavy and go back through it later. And like I wrote earlier, you won't find a better introduction to the mathematical material than here.
Carroll should be given the Nobel prize for this book. If not in Physics, then in literature. I'd give this textbook 10 stars if I could. | | Spacetime and Geometry: An Introduction to General Relativity by Benjamin Cummings A nice blend of the ideas of physics with mathematics | Kudos to Carroll.
This book is an excellent INTRODUCTION to SR and GR for the graduate physics student as well as the graduate mathematics students.
Pure mathematics often loses sight of the ideas which motivated it and physics often loses the mathematical foundations from which it is built.
This book offers some level of mathematical formalism to the physics student while exposing the ideas motivating the mathematical concepts.
I particularly like how he builds up the mathematical machinery of GR by introducing sets then topology on this set giving a topological space. Now he adds in the ideas of a manifold which make this topological space look like Rn locally with the patches sewn together smoothly. The manifold comes equipped with tangent space, cotangent spaces and their product spaces giving tensor spaces. These are defined nicely with reference to component formalism as well as the multilinear algebra approach as maps from products spaces to the reals, etc. He delves into forms and tantalized the reader with deRham cohomology although doesnt go into it. He shows how these can be differentiated ( exterior derivative ) and integrated.
Now the metric is introduced giving a geometry. To this is added a connection which is independent of the metric and leads to notions of parallel transport and differentiation of tensors ( covariant derivative ). One sees that in a special case one can derive a unique connection from the metric ( Levi-Cevita ) which is used in GR.
Fibre bundles, Lie derivatives, pullbacks etc are introduced as needed.
He then presents some introductory GR material by applying the mathematics.
| | Spacetime and Geometry: An Introduction to General Relativity by Benjamin Cummings Great Book But Won't Get You To The Promised Land | 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. | | Spacetime and Geometry: An Introduction to General Relativity by Benjamin Cummings good math chapters, not at beginner's level after that |
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.
Please keep in mind my review is from a beginner point of veiw. Readers more experienced in GR may feel different but that book is supposedly written for beginners right?
The math chapters 2 and 3 are worth reading because they 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 is nice that the book makes a difference between a Christoffel connection and a generic connection. The appendices are worth reading too cause they will give you a feeling for some new to you math necessary for GR 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. Also 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 practise.
There are problems after each chapter but not the necessary beginners problems that increase your conceptual understanding of the theory. Instead, some of the problems 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. Solving these by hand proves that you can take derivatives and you are a mazochist but not that you understand GR. Other problems are really relevant to your education but are not dirrectly connected to the discussion in the text. Because of that you have to solve them from scratch and it will take you ages ...
If you are a beginner like me, you should read the math chapters and all appendices of Carroll's book plus chapter 4. Then you should read a real book for beginners with a lot of examples how to apply GR in real calculations and how to understand it. For that I recommend James Hartle's "Gravity: An Introduction to Einstein's General Relativity" and Bernard Schutz's "A first course in General Relativity". After that hopefully you will understand the rest of Carroll's book better. My experience was that often I had to read Hartle's book in order to understand and solve a problem in Carroll's book.
| | Spacetime and Geometry: An Introduction to General Relativity by Benjamin Cummings Product Description | | 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. |
| |
