Einstein-Cartan Field Equations Derivation

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SUMMARY

The discussion focuses on the derivation of the Einstein-Cartan Field Equations through the variation of the Einstein-Hilbert Action. A specific resource, the paper available at arxiv.org/abs/0911.0334, is highlighted as a comprehensive reference that provides both geometric preliminaries and the detailed derivation sought by the participants. The conversation emphasizes the importance of consulting references for deeper understanding.

PREREQUISITES
  • Understanding of the Einstein-Hilbert Action
  • Familiarity with the Torsion Tensor in differential geometry
  • Basic knowledge of General Relativity principles
  • Experience with mathematical derivations in theoretical physics
NEXT STEPS
  • Study the Einstein-Hilbert Action in detail
  • Research the properties and applications of the Torsion Tensor
  • Explore advanced texts on General Relativity and its extensions
  • Review the paper at arxiv.org/abs/0911.0334 for a complete derivation
USEFUL FOR

The discussion is beneficial for theoretical physicists, graduate students in physics, and researchers interested in advanced topics in General Relativity and geometric theories of gravity.

Physicist97
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I'm looking for a derivation of the Einstein-Cartan Equations from varying the Einstein-Hilbert Action. I've looked around the internet but can't seem to find one, so if anyone knows of a pdf or book reference that goes through the derivation, that would help a lot. The wikipedia page for Einstein-Cartan Theory mentions the equations being derived by varying the Einstein-Hilbert Action with respect to the Torsion Tensor, but does not go into any detail.
 
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Well, right from the references for that article, the following gives geometric preliminaries and the derivation you seek:

http://arxiv.org/abs/0911.0334
 
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Likes   Reactions: Physicist97
Thank you! Lesson learned, always check the references :) .
 

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