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The modern LargeScale Structure of Spacetime book 
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#1
Oct2707, 09:37 AM

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Ever since I started reading Hawking's classic "LargeScale Structure of Spacetime", written in 1973, I always wished that there was a more uptodate book on general relativity that uses the book's level of mathematical rigour. But every modern book used less mathematics than I wanted to see. Well, I think here it is:
http://www.amazon.com/EinsteinsGene...9485666834230 Released in May 2007, 540 pages. No reviews yet. The book description says "The book contains a thorough introduction to tensor calculus and curved manifolds. After the necessary mathematical tools are introduced, we give a thorough presentation of the theory of relativity. Also, some advanced topics not previously covered by textbooks; e.g. KaluzaKlein theory, Israel's formalism and branes. Anisotropic cosmological models are also included. The book contains a large number of new exercises and examples, each with separate headings. The reader will get an updated introduction to general relativity including the most recent developments in cosmology." The table of contents shows the mathematics used, which seems about the same as Wald's book from 1983. But it still doesn't use more advanced diferential geometry topics as Hawking's book (e.g. fiber bundles), but it seems close enough. Any opinions? 


#2
Oct2807, 12:16 PM

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#3
Oct2807, 02:15 PM

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Ludvigsen's text is nice and concise.
Another text to consider is deFelice & Clarke. Of course, none of these are replacements for Hawking & Ellis. (By the way, these are all published by Cambridge University press. It might make a nice little project to trace the lineage ("schools of thought") of the various relativity books... Cambridge, Princeton, Chicago, Syracuse, Toronto, etc... ) ) 


#4
Oct2807, 03:00 PM

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The modern LargeScale Structure of Spacetime book
I concur that de Felice and Clarke offer some unique and valuable insights! In fact, I just was rereading part of that book as recently as yesterday (in connection with the principle null congruences in the Kerr vacuum).
From time to time I express my mixed feelings when I consider that so few publishers of serious mathsci books these days make any attempt to address the needs of students. Cambridge University Press consistently brings out good to excellent books while keeping the price reasonable, at least in comparison to many other profit hungry publishers (some of these incorrigibly nasty publishers I mean huge multinationals, not some crank in his garage have made a concerted effort to silence their critics, which is truly deplorable!) 


#5
Oct3107, 09:16 PM

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Here's another [library] book on my shelf...
Spacetime: Foundations of General Relativity and Differential Geometry by Marcus Kriele http://www.amazon.com/SpacetimeFoun.../dp/3540663770 (you can look inside) This is published by Springer. 


#6
Oct3107, 10:07 PM

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#7
Oct3107, 10:29 PM

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Find it in a library...
http://www.worldcatlibraries.org/wcpa/top3mset/42391590 or parts of it from google http://books.google.com/books?isbn=3540663770 


#8
Nov107, 06:01 PM

P: 363

A perfect book! And in the spirit of my earlier thread:
http://www.physicsforums.com/showthread.php?t=192119 


#9
Nov207, 02:11 AM

P: 900

Ouch, that Springer book has what I'd call "institutional" pricing. Definitely not priced for mac & cheese eating grad students.
Another Springer book that is strong mathematically is by Norbert Straumann, but it's not cheap, either. I'll third the Felice & Clarke book. They take particular care with notation so that nothing is ambiguous. 


#10
Nov207, 07:20 AM

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In the preface to Kriele's book,
( follow the google link: http://books.google.com/books?isbn=3540663770 and search for "Australian", then follow the link to page xi ... alternatively, google: "two Australian relativity students" ) there is a dedication which reads: "This book is dedicated to two Australian relativity students who on their way to gaining their doctorates courageously stood up against the immoral behavior of their supervisor and the highhandedness of their university." Anyone know the story behind this? 


#11
Nov607, 04:58 PM

P: 32

A book that has the same spirit as Hawking and Ellis (utilizing topology to study casaul structure) is the following by Joshi
http://www.amazon.com/AspectsGravit...4389680&sr=81 For methods in GR that you won't find elsewhere try Poisson http://www.amazon.com/AspectsGravit...4389680&sr=81 And if you're interested in black hole physics try Frolov and Novikov. It's very hard to find and prohibitively expensive. http://www.amazon.com/BlackHolePhy...4389766&sr=11 


#12
Nov707, 12:36 PM

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I'll second the book by Poisson (or maybe you were seconding my recommendation, since I mentioned it recently in some other threads!). Frolov and Novikov is a gold mine of information for that price, you'd think they could have made the pictures a bit larger! but certainly not the best choice for a first or even a second book (but if you can find it in your local research library, go for it!). My favorite topic in F&N is the fine discussion of Vaidya thought experiments. I haven't seen the book by Joshi but would expect it would be good, and might even include discussion of Vaidya null dust, which is by far the most important exact solution which many students don't learn in a first gtr course!



#13
Mar408, 02:04 AM

P: 4

I don't know of you guys but let me tell you there is no book ever written on General Relativity better than the classic book Gravitation by Wheeler, Misner, Thorne; which not only covers all of general relativity but has many chapters devoted completely to concrete mathematics like Differential Geometry and book is over 2000 pages of material on Gravitation only check out in library before thinking to buy as it is a mammoth book on the subject and has taught General Relativity to all the new generation of Relativist



#14
Jul1910, 10:22 AM

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Gravitation is not at the same level as the ones discussed here; it is an introduction.



#15
Jul1910, 12:27 PM

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#16
Jul1910, 01:28 PM

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Oh, apologies! I came at this thread via the "similar threads", hadn't noticed that it was so old.



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