Einstein's gravity does not incorporate the "spinor" nature of fermions. The tetrad formulation or Cartan's theory is suggested as the way to go around this problem - by allowing the spin connection to have torsion. It is known that the spin couples with the torsion.
Please suggest some references where this "spin-torsion coupling" has been discussed in details. Specifically, some concrete examples of calculations where one can see this "coupling" term(s) explicitly.
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