Relativity and Cosmology Booksreviewed by T. Nelson
This is a great description of relativity with all the interesting scientific stuff meticulously squeezed out of it, leaving only the math.
That is good. You cannot understand relativity or cosmology, or even talk about them intelligently, without understanding the math. Relativity is actually not difficult, but lots of people have trouble with it because they've never used tensor calculus.
The authors explain tensor calculus in a very straightforward manner with no dumb jokes, no chit-chat, and without excessive formality. The authors say no steps in the derivations are skipped. This isn't really true; in many places several steps are combined, which is a lot like skipping steps. However, only in a few places do they pull solutions out of what Donald Trump would call their ‘wherever.’
As a result, the book is almost solid math from cover to cover. Mainly it teaches how to manipulate the symbols, not their physical meaning or their implications. That is deliberate: you need to develop the ability to figure out meanings from the equations. A few things could be defined better for beginners. Although it's aimed at students, even a beginner, with some effort and an Internet connection, and a background in calculus and linear algebra, should be able to make sense of it.
Those 263 pages will go slow for a beginner and they might require some effort and, perhaps, a little caffeine, but if you make the effort, this book will give you confidence to read some of the most exciting stuff ever written: cosmology, gravitation, and relativity. Students will find it essential.
To make the book more interesting, the authors have tacked on a couple chapters on cosmology for the second edition. Many readers will skip those and move on to a more complete cosmology text, of which the best is unquestionably Steven Weinberg's Cosmology. But I recommend reading Dodelson, which combines the observational data with the theory, first. If you've read Dalarsson & Dalarsson, Dodelson is just straightforward science. By the time you're finished with that, Weinberg will hopefully be in a second edition or (as is more likely for me) the universe will have gone into heat death and it will all be academic. Weinberg's 1972 General Relativity and Cosmology is also good. Used copies of the 2008 paperback edition are still around. A new book, Introduction to General Relativity, Black Holes and Cosmology by Yvonne Choquet-Bruhat, is an introduction to the physics for mathematicians.
There is no erratum list that I could find. Finding the errors in the book has been left as an exercise for the reader, but there aren't many.
aug 28, 2015
This one derives relativity by analogy to Maxwell's equations, then derives it by analogy to Newton's theory, and then derives it again for real. Each section gradually gets a little more difficult. The authors make a good effort to include experimental evidence, and they take more time to explain what the tensors actually look like, but they waste a tremendous amount of time on the linear approximation, which is the simplified form of general relativity for spacetime in the absence of strong gravitational fields. By the time you get to the real theory, you're utterly worn out. The writing is also marred by excessive political correctness.
feb 07, 2016
This is a great book for those who are interested in the astrophysical evidence as well as the equations. Not all the equations are derived, but it's very readable and reasonably easy to follow. There is a thorough errata list here.
Disclaimer: I am only halfway through this one.
This book is more mathematically oriented, and like a math text it's full of propositions, lemmas, and exercises. This is not necessarily a bad thing: we can't complain when one author pulls equations out of a hat and then complain when another goes and derives them. But the style here is rather brusque, even for a math book.
On page 214, discussing dark energy, the author says without qualification “it has recently been found that baryonic matter itself represents at present only about 4% of this energy content.” Mathematicians will like this, but astrophysicists will recognize that there's a ton of evidence behind it; an astrophysics book like Dodelson will be helpful in understanding that evidence and the uncertainties behind this statement.
Disclaimer: I have not yet finished this one.
The best way to understand something is to explain it to someone else. So when Nobel-prize-winning particle physicist Steven Weinberg got curious about cosmology, he wrote the definitive book on the subject, much to the consternation of his colleagues. Even though he derives nearly every equation, it's not just mathematics here: Weinberg relates the findings to subatomic particles and to astrophysical evidence wherever possible. There are even a few graphs. Weinberg's writing style is the clearest I have ever seen. Like his books on QFT, Cosmology is magnificent.
Disclaimer: I have not yet even started this one.
This classic text has big sections on cosmology, but its main strength is general relativity, which it covers in the first 590 pages. Subsequent sections discuss relativistic stars, cosmology, gravitational collapse, gravitational waves, and experimental tests on general relativity. The sections on relativity are still great, but the later sections are somewhat out of date. It's not as difficult as the other books above, but at 1279 pages and 5.4 pounds just for the paperback version let's just say that I'm not taking this one to the beach.
Disclaimer: I ... um, lost my copy.
This book is the opposite of Choquet-Bruhat. It's the only one that teaches general relativity without using tensors. The author discusses the scientific evidence at each step. The idea is for the student to understand the concepts first. Tensors are then introduced starting on page 279, and you only get 76 pages of them. For Cheng it's the cosmology and astrophysics, not the formal math, that are important.