Derivation of Einstein Cartan theory from General Relativity

TL;DR

This paper derives the Einstein Cartan theory from classical general relativity through discrete and continuum approaches, highlighting EC's ability to model angular momentum exchange beyond GR.

Contribution

It presents novel derivations of EC field equations from GR using Kerr solutions and mass distributions, connecting the two theories.

Findings

EC can be derived from GR via discrete torsion and spin fields.

Continuum limit of Kerr mass distributions yields EC field equations.

EC models angular momentum exchange not possible in GR.

Abstract

This work derives the elements of classical Einstein Cartan theory (EC) from classical general relativity (GR) in two ways. (I) Derive discrete versions of torsion (translational holonomy) and the spin torsion field equation of EC from one Kerr solution in GR. (II) Derive the field equations of EC as the continuum limit of a distribution of many Kerr masses in classical GR. The convergence computations employ epsilon delta arguments, and are not as rigorous as convergence in Sobolev norm. Inequality constraints needed for convergence restrict the limits from continuing to an infinitesimal length scale. EC enables modeling exchange of intrinsic and orbital angular momentum, which GR cannot do. Derivation of EC from GR strengthens the case for EC and for new physics derived from EC.