As I was working through this article by Bronnikov regarding Einstein–Cartan theory:
Bronnikov, K. A., & Galiakhmetov, A. M. (2015). Wormholes without exotic matter in Einstein–Cartan theory. Gravitation and Cosmology, 21(4), 283–288. doi:10.1134/s0202289315040027
He discusses a stress energy tensor and an effective stress energy tensor see his (10). It is a non-minimally coupled scalar field reproduced here for convienece:
$T^{(eff)}_{ab}[\phi]=T_{ab}[\phi]+\kappa^{-1}\Lambda_{ab}$
Where $\Lambda_{ab}$ is a spin piece, and $\kappa$ is the Einstein field equation constant. My question is, what makes this important? To clarify, there are still pieces in $T_{ab}[\phi]$ which couple to spin, so it is not like we have completely broken those pieces off. $\Lambda_{ab}[\phi]$ is a piece made only/entirely from spin.
Any thoughts either mathematical or physical would be greatly appreciated! Anything that you think would help clarify please ask! Thanks! ^^
P.S. The following post discusses ECSK theory and some of the relevant topics. Thought it might help! Spacetime Torsion, the Spin tensor, and intrinsic spin in Einstein-Cartan theory
