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Can someone please recommend books that deal with the techniques used to apply General Relativity at Global scales? Einstein's Field Equations are local statements, so is there a technique or a whole book that deals with how to get global information using them?

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The book by Hawking and Ellis, The large-scale structure of spacetime, or Wald's general relativity may be what you are looking for.

Global methods in GR were used by Roger Penrose in the sixties to establish the singularity theorem of black holes, and are a combination of topological techniques. These methods were further expanded by Hawking and Penrose to prove that the big bang is a space-time singularity, and further employed by Hawking to establish the properties of the absolute horizons of black holes.

Rather understandably, the book by Hawking and Ellis, which was written in 1973, draws much material from Hawking's pioneering work on the topic, while Wald's book is a self-contained, slightly more modern introduction to much of the same material and techniques.

Since then, global methods have become a major topic of research, at the frontier between mathematics and physics. Depending on your level of sophistication you may read either a chapter like Causal structure and global geometry in Wikipedia, or some rather nice lecture notes given at Columbia. Just remember to brush up on your understanding of Raychaudhuri's equation ;-)

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  • $\begingroup$ Wald is not self-contained, he does not prove the singularity theorems or Geroch's theorem (he has a sketch). $\endgroup$ – Ryan Unger Jan 17 '17 at 16:49
  • $\begingroup$ @0celo7 That imples it is not complete, not self-contained. $\endgroup$ – MariusMatutiae Jan 17 '17 at 16:51
  • $\begingroup$ merriam-webster.com/dictionary/self%E2%80%93contained "complete in itself" $\endgroup$ – Ryan Unger Jan 17 '17 at 17:19
  • $\begingroup$ @0celo7 Normally, by self-contained one means needing no previous foundation, i.e. built from the ground up. It is unavoidable a book is somewhat open-ended. But I do stand corrected, I only meant self-contained in this sense. $\endgroup$ – MariusMatutiae Jan 17 '17 at 17:35

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