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Ta-Pei's book is MUCH better than Sean Carroll's textbook
on November 26, 2013
I am a physics graduate student without pre-knowledge about GR, and I must say:
The Ta-Pei's book called <<Relativity, Gravitation and Cosmology: A Basic Introduction >> is MUCH better than Sean Carroll's textbook <<An Introduction to General Relativity: Space and Geometry>>, simply because the Ta-Pei's book provides much more detailed and rigorous explanation with more illustrative diagrams than what the Sean's book does.
For example, Ta-Pei book provides two different ways to derive the Geodesic equations on the page 88, 106 and 320, whereas Sean is only able to provide one way to derive it on the page 105. I always want to know how the Geodesic equation is related to the Lagrange. and Ta-Pei's book explains this very well, whereas Sean does not explain anything about it.
Many description on Sean is unclear. He tends to omit many intermediate steps, for example, on the page 137, he omits a lot steps to derive the equation (3.178). Another example, on the page 161, he says that it is straightforward to have equation (4.56). At least not straightforward to me. He assumes that every readers are geniuses or have plenty of time to figure out what he says. Clearly, he excludes those non-geniuses, like me, from reading his book.
He tries to teach me how to do GR by using Differential Geometry without systemically teaching me how to do Differential Geometry. This causes me to waste lots of time to figure out what Sean's book actually means. For example, Sean is awful to explain what "One-form" means. Rather than introducing such complicated concept from Differential Geometry, Ta-Pei teaches me how to do GR by introducing highly self-contained mathematical concept. In Ta-Pei's way, I do not have to look for more advanced math textbooks in order to understand what he really means. This saves me enormous amount of time. Some description on Ta-Pei is marvellous. For example, on the top of the page 147, "the roles of time and space are interchanged when crossing over the r=r*." This concise description captures the whole feature of the event horizon! That is awesome!
In contrast to Sean's book, I also like the diagrams on Ta-Pei's book, for example on the page 106 the fig 6.3, which is simple but means a lot to me. Another example, fig 7.1 on the page 123, which helps me to understand worm hole.
Ta-Pei's book provides detailed solutions to almost all the exercise questions (Including the Review questions in the end of each chapters). This is so great. I learnt a lot how to solve GR problems from him. In contrast, Sean's textbook does not provide any solution - clearly, Sean does not care about teaching, and is a lazy or busy teacher.
Ta-Pei's book is an intermediate level on GR. Sean's book is a little more advanced than Ta-Pei's book. However, Readers who finished Ta-Pei's book could continue to read more advanced GR book without touching Sean's book. So please do not waste time on Sean's book IF you had no pre-knowledge about GR before! My honest suggest! If you had some experience or exposure to GR or Differential Geometry, then Sean's book may be for you to read.