Worked examples Cartan Formalism

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Discussion Overview

The discussion centers around seeking additional examples and resources related to the Cartan formalism, particularly in the context of calculating connection one forms and curvature two forms. Participants share various references and resources that may aid in understanding and applying these concepts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant expresses a need for more examples of the Cartan formalism to verify their calculations, specifically looking for video, notes, or books.
  • Another participant suggests several resources, including Sean Carroll's "Spacetime and Geometry," which covers an expanding universe, and mentions Jetzer's lectures on the Schwarzschild case.
  • Additional resources are provided, including lecture notes by Matthias Blau and Wald's book on General Relativity, which also discusses the Schwarzschild solution.
  • Links to specific metrics for examples are shared, including Schwarzschild and Robertson-Walker metrics, along with resources on differential forms related to connections and curvature.
  • A link to a PDF on Cartan formalism is provided, highlighting a section with numerous examples.

Areas of Agreement / Disagreement

Participants generally agree on the availability of various resources and examples related to the Cartan formalism, but no consensus is reached on a specific example that the original poster is looking for.

Contextual Notes

The discussion does not clarify whether the provided resources fully meet the needs of the original poster, nor does it address any assumptions or limitations regarding the examples shared.

Who May Find This Useful

Individuals studying the Cartan formalism, particularly those seeking additional examples and resources for understanding connection one forms and curvature two forms in the context of general relativity.

zwoodrow
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TL;DR
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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