A Worked examples Cartan Formalism

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looking for worked examples of cartan formalism calculation of one form connections and two form connections
I am learning the cartan formalism from the book Relativity Demystified. It has a few examples. I am looking for more examples in video, notes, or books of the work calculations of the connection one forms and the curvature two forms to check my calculations against. My search so far has turned up not much. Thank you
 
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Sean Carroll (Spacetime and Geometry) does the simple case of an expanding universe in his Appendix J.

Jetzer does the Schwarzschild case in his lectures. (I can't find a simple direct link -- just google for Jetzer and "advanced topics in GR".)

Matthias Blau does Schwarzschild and Kaluza Klein in his lecture notes (which are, imho, good for other things as well at a more advanced level).

Wald also does Schwarzschild in his book "General Relativity".

Is there a particular example you wanted?
 
 

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