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Rating: 
Summary: The only book for advanced GR
Review: Although it seems to be a general relativity book, this is actually an excellent book for learning advanced mathematics. The sections on differential geometry and spinor analysis rival any of the dedicated textbooks on these subjects. This is also the only book to give a clear and concise introduction to tetrads and the Newman-Penrose formalism of general relativity.
This book is a must for any serious physicist.
Rating:
Summary: treasure trove of knowledge
Review: It seems to me that there are far too many in number, and far too few in quality, books on on general relativity.John Stewart, rather than waste time on the hordes of cute little cartoon models apt for a tourist rather than physicist, gets straight to the heart of the matter and presents amazingly powerful results (on differential geometry/ Spinors/ Asymptopia/Initial Value Problem). He doesn't skip any steps in his proofs and doesn't try to appeal to science fiction intuition. As someone who hasn't encountered spinors before reading this book, I'm grateful for the helpful appendi on the matter. Unfortuneately however I've found in different books the notation for spinors can vary wildly. The result is that I must refigure out all the basic properties to understand the notation. My complaint is that Stewart doesn't seem* (perhaps it's my ignorance) to use the most common notation, but on the other hand, he also provides the most easily used and referenced appendix. In summary, if reading most of that relativity tripe make you a tourist, Stewart makes you a citizen.
Rating:
Summary: A short and sweet treatment of many subjects
Review: John Stewart has written a beautiful book that does indeed face many of the advanced subjects of General Relativity. Following an introduction that will prove useful to readers with no knowledge of GR, the author includes detailed but affordable discussions of advanced subjects including: 1. the Newman Penrose formalism and classification of exact vacuum solutions, 2. physical and mathematical concerns of asymptotic behaviors which are particularly appropriate for workers interested in gravitation wave observations, 3. spinors in general, and 4. the quasi linear PDE of Einstein's equation. In short, every relativist or researcher interested in relativistic results should find the time to review this text.
Rating:
Summary: Excellent
Review: This is an excellent book (mostly) about the use of spinorial methods in GR. However it is quite difficult, and the author recommends that you try Chandrasekhar or Hawking & Israel first. There is an introductory chapter on the basics of differential geometry which is good but no great shakes, and a lovely short chapter on spinors, Goldman-Sachs, Robinson's theorem, and the NP formalism etc. After that it only gets better. The third chapter is an extraordinarily careful treatment of asymptotics and the fourth is on the *characteristic* initial value problem (ie. on null hypersurfaces---*not* the general cauchy problem!). If you think either of these topics comprises what you've read in MTW, prepare for a surprise!A word of warning, Stewart is a mathematician and it shows. The rigour is splendid---this is real scholarship. The author also edits Clas. & Q. Grav.
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