Affine defects and gravitation (Q5932496)

The author argues that the structure of General Relativity (GR) as a theory of affine defects is deeper than the standard interpretation as a metric theory of gravitation. There exist arguments that: (i) Einstein-Cartan theory (EC) should be the standard-bearer for GR-like theories; (ii) EC is a theory of affine defects whose natural variational principle is the Palatini variation with respect to generalized connection coefficients (not with respect to the metric); (iii) physically, EC almost certainly describes discrete affine defects. A discrete affine interpretation of EC and gauge theory yields topological definitions of momentum and spin (and Yang-Mills current), and their conservation laws become discrete topological identities. Considerations from quantum theory provide evidence that discrete affine defects are the physical foundation for gravitation.