Help me learn the GR cartan formalism

[zwoodrow]

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?
thanks

 

[shoehorn]

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.

 

[Ben Niehoff]

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.