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Help me learn the GR cartan formalism

  1. Apr 23, 2010 #1
    Im learning the cartan formalism of doing quick computations of the christoffel symbols and curvature however my book is a bit vague (McMahon). Does anyone have any lecture notes or webpages that do a good job?
  2. jcsd
  3. Apr 24, 2010 #2
    Pretty much all of the standard graduate-level books cover this at an acceptable level. Ones that spring to mind immediately include Wald, MTW, et al. I think even Sean Carroll's book discusses it as well.

    Actually, now that I think of it, Chandrasekhar's book on black holes covers this in quite some detail, including the explicit Newman-Penrose formalism. It's very index-heavy though, so if you're inclined towards coordinate-freedom in your geometry, you might not like it very much.
  4. Apr 27, 2010 #3

    Ben Niehoff

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    MTW actually has a decent discussion of it, including a worked example.

    Also, I think Nakahara's discussion is very concise and clear. He takes only a few pages to cover it, but he makes it absolutely clear how to carry out a calculation, and how to relate the connection form to the traditional Levi-Civita connection.

    The Cartan structure equations can actually be solved explicitly without too much difficulty, giving you expressions for the connection and curvature in terms of frames, co-frames and their derivatives.
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