  We derive the Schr\"{o}dinger-Newton equation as the non-relativistic limit
of the Einstein-Dirac equations. Our analysis relaxes the assumption of
spherical symmetry, made in earlier work in the literature, while deriving this
limit. Since the spin of the Dirac field couples naturally to torsion, we
generalize our analysis to the Einstein Cartan-Dirac (ECD) equations, again
recovering the Schr\"{o}dinger-Newton equation.
