Penrose diagrams, reference request.

[martinbn]

Where can one find a general and detailed exposition of Penrose diagrams? What I have seen so far, in the books, are relatively brief general comments and a couple of specific examples. Usually Minkowski and Schwarzschild metrics, sometimes one or two more.

 

[bcrowell]

I like the discussion in Penrose's popularization Cycles of Time. The good thing about it is that although it's nonmathematical, he explains lots and lots of examples.

For a more detailed mathematical treatment, you could try Hawking and Ellis, or Winitzki's online book http://sites.google.com/site/winitzki/index/topics-in-general-relativity . Winitzki has nice discussions of things that I haven't seen elsewhere, like the properties that are required for the mapping in the Minkowski case. (E.g., Hawking and Ellis just give a mapping, but they don't say anything about why they choose that particular one.) Wald has a careful, detailed mathematical treatment of the definition of asymptotic flatness.

What I find hard about the subject is that it seems to have undergone a process of gradual generalization, but Penrose's is the only attempt I've seen to go back and give a synoptic view, and Penrose's treatment is nonmathematical. I haven't seen a clear, mathematically detailed description of what the fundamental principles are that apply in general. Everybody just presents certain special cases.

 

[martinbn]

Thanks, this is actually helpful.

What I find hard about the subject is that it seems to have undergone a process of gradual generalization, but Penrose's is the only attempt I've seen to go back and give a synoptic view, and Penrose's treatment is nonmathematical. I haven't seen a clear, mathematically detailed description of what the fundamental principles are that apply in general. Everybody just presents certain special cases.

Yes, I have looked at only a few books, but this was my impression too, and I would like to see a mathematically detailed description.

The book of Penrose is on my "to read" list, now I will bump it up. I have looked at Hawking and Ellis, but that part wasn't to my liking. Probably I wasn't ready for it yet. I'll give it another try. Winitzki's books, on first glance, seems exactly what I was looking for, and I have immediate access to it. It'll certainly help me understand better.

Thanks a lot.