Spinors and torsion in general relativity

Abstract

Conformal rescalings of spinors are considered, in which the factor Ω, in εAB {mapping}ΩεAB, is allowed to be complex. It is argued that such rescalings naturally lead to the presence of torsion in the space-time derivative ▽a. It is further shown that, in standard general relativity, a circularly polarized gravitational wave produces a (nonlocal) rotation effect along rays intersecting it similar to, and apparently consistent with, the local torsion of the Einstein-Cartan-Sciama-Kibble theory. The results of these deliberations are suggestive rather than conclusive. © 1983 Plenum Publishing Corporation.