General relativity with spin and torsion: Foundations and prospects.

*(English)*Zbl 1371.83017Summary: 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 U4 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 U4 theory arises as a local gauge theory for the PoincarĂ© group in space-time. The deviations of the U4 theory from standard general relativity are estimated, and the prospects for further theoretical development are assessed.

##### MSC:

83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |