In GR we use the Riemannian manifold without any torsion to describe the theory. Hence, the geodesic equation can be interpreted as "a trajectory of a free falling particle" or "equation of motion". But in Einstein-Cartan manifold the torsion prevents us to use the geodesic equation as an equation of motion. So, my question is that, what is the meaning of a geodesic equation in this theory?
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