Nonrelativistic limit of Einstein-Cartan-Dirac equations

Abstract

We derive the Schrödinger-Newton equation as the nonrelativistic limit of the Einstein-Dirac equations. Our analysis relaxes the assumption of spherical symmetry, made in an 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 equations, again recovering the Schrödinger-Newton equation.