General relativity with spin and torsion: Foundations and prospects

TLDR

The paper extends Einstein’s theory by incorporating matter spin, which couples to spacetime torsion (Cartan’s tensor). The authors aim to review theoretical evidence supporting the inclusion of spin and torsion in relativistic gravity. They analyze the U4 theory as a local gauge theory of the Poincaré group and assess its deviations from standard general relativity. The U4 theory predicts a weak spin‑contact interaction, arises as a local gauge theory, and its deviations from GR are quantified with prospects for further development.

Abstract

A generalization of Einstein's gravitational theory is discussed in which the spin of matter as well as its mass plays a dynamical role. The spin of matter couples to a non-Riemannian structure in space-time, Cartan's torsion tensor. The theory which emerges from taking this coupling into account, the ${U}_{4}$ theory of gravitation, predicts, in addition to the usual infinite-range gravitational interaction medicated by the metric field, a new, very weak, spin contact interaction of gravitational origin. We summarize here all the available theoretical evidence that argues for admitting spin and torsion into a relativistic gravitational theory. Not least among this evidence is the demonstration that the ${U}_{4}$ theory arises as a local gauge theory for the Poincar\'e group in space-time. The deviations of the ${U}_{4}$ theory from standard general relativity are estimated, and the prospects for further theoretical development are assessed.