Non-relativistic limit of Einstein-Cartan-Dirac equations

Abstract

We derive the Schrödinger-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 Schrödinger-Newton equation.

arXiv commentV3: 22 pages, typos and language corrected, clarifying paragraphs added, references added, accepted for publication in Phys. Rev. D

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Cited by in corpus (4)

• Fermions on curved backgrounds of matrix models
• Einstein-Cartan-Dirac gravity with $U(1)$ symmetry breaking
• Cosmological bounces, cyclic universes, and effective cosmological constant in Einstein-Cartan-Dirac-Maxwell theory
• Torsion-Driven Nonlinearity in Spinless Quantum Mechanics