The modern "Large-Scale Structure of Spacetime" book Ever since I started reading Hawking's classic "Large-Scale Structure of Spacetime", written in 1973, I always wished that there was a more up-to-date 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/Einsteins-Gen...95/ref=si3_rdr_bb_product/103-2948566-6834230 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. Kaluza-Klein 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?
Books which are "successors" to Hawking & Ellis? Have you seen the book by Malcolm Ludvigsen, General Relativity: a Geometric Approach, Cambridge University Press, 1999? This is a short book at a level comparable to Carroll, Spacetime and Geometry and other recent gtr textbooks, but it offers an excellent discussion of connecting vectors, optical scalars, future null infinity, and other topics which elaborate/extend some topics discussed in Hawking and Ellis. And what about Eric Poisson, A Relativist's Toolkit, Cambridge University Press, 2004? This short book again has similar prerequisites to Carroll, but focuses on elaborating/updating the discussion of Hawking and Ellis of black holes. I haven't seen this book yet, but I often cited Gron's review paper on the Ehrenfest "paradox" (incidently, the kinematical decomposition discussed in H&E is very useful there!), and I have generally found that each textbook has some unique virtues. However, from your description I don't see why you think this book is intended to pick up where Hawking and Ellis left off. For that I suggest rather some of the long and excellent review articles by Ellis on cosmological models which have appeared in various places over the years, including this one in the arXiv, for cosmological applications, plus the two books I cited above, for conformal structure, optical scalars, kinematic decomposition, and black hole mechanics.
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... ) )
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!)
Here's another [library] book on my shelf... Spacetime: Foundations of General Relativity and Differential Geometry by Marcus Kriele http://www.amazon.com/Spacetime-Foundations-Relativity-Differential-Monographs/dp/3540663770 (you can look inside) This is published by Springer.
Hey, I like the level of math in this book. Thanks for the referral. How did I miss this for the past 8 years?
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
A perfect book! And in the spirit of my earlier thread: https://www.physicsforums.com/showthread.php?t=192119
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.
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?
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/Aspects-Gravi...8312129?ie=UTF8&s=books&qid=1194389680&sr=8-1 For methods in GR that you won't find elsewhere try Poisson http://www.amazon.com/Aspects-Gravi...8312129?ie=UTF8&s=books&qid=1194389680&sr=8-1 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/Black-Hole-Ph...8312129?ie=UTF8&s=books&qid=1194389766&sr=1-1
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!
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
Re: The modern "Large-Scale Structure of Spacetime" book Gravitation is not at the same level as the ones discussed here; it is an introduction.
Re: The modern "Large-Scale Structure of Spacetime" book You wait two years before breaking this to him?
Re: The modern "Large-Scale Structure of Spacetime" book Oh, apologies! I came at this thread via the "similar threads", hadn't noticed that it was so old.