Derivation of Einstein-Cartan theory from general relativity

This paper 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.

Automated summary

This paper derives the elements of classical Einstein-Cartan theory (EC) from classical general relativity (GR) in two ways: using one Kerr solution in GR and a distribution of many Kerr masses in GR. The limitations in convergence computations restrict the limits from continuing to an infinitesimal length scale, impacting the derivation of EC from GR. EC enables modeling exchange of intrinsic and orbital angular momentum, strengthening the case for EC and new physics derived from EC.