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I'm currently studying on how to write GR as a CS theory, but i have a problem with one of the basic theorem of this subject.

$$ e^\mu_{\ \ a} \epsilon^{\nu \rho \sigma} R_{\ \ \rho \sigma}^a = \det(e) G^{\mu\nu} $$

And i don't know how to prove. Any help is welcome :)

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  • $\begingroup$ Can you expand your question. What is CS theory? $\endgroup$ – MBN May 19 '18 at 15:56
  • $\begingroup$ Chern-Simons , a gauge field theory $\endgroup$ – user184173 May 19 '18 at 19:37
  • $\begingroup$ where did you find this theorem and more generally : where are you studying cs theory from? $\endgroup$ – magma May 20 '18 at 23:37