Derivation of EinsteinCartan theory from general relativity
Abstract
This paper derives the elements of classical EinsteinCartan theory (EC) from classical general relativity (GR) in two ways. (I) Derive discrete versions of torsion (translational holonomy) and the spintorsion 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 “epsilondelta” 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.
 Publication:

International Journal of Geometric Methods in Modern Physics
 Pub Date:
 2021
 DOI:
 10.1142/S0219887821500833
 arXiv:
 arXiv:1301.1588
 Bibcode:
 2021IJGMM..1850083P
 Keywords:

 General relativity;
 Einstein–Cartan theory;
 affine torsion;
 spin;
 angular momentum;
 04.20.Cv;
 04.50.Kd;
 Fundamental problems and general formalism;
 Modified theories of gravity;
 General Relativity and Quantum Cosmology
 EPrint:
 44 pages, 1 table, 63 equations, 3 figures, 93 lines of computer algebra, 37 references, 7 Appendices. This version Adds a postpublication note the responds to some commentaries about the paper