Spin and Anholonomy in General Relativity

TL;DR

This paper explores how spin interacts with the geometry of spacetime in General Relativity, revealing that what appears as torsion is actually a manifestation of tetrad anholonomy, with implications for teleparallel gravity.

Contribution

It clarifies the relationship between torsion and anholonomy in General Relativity and its teleparallel equivalent, highlighting the geometric origin of torsion as frame anholonomy.

Findings

Torsion couples to Dirac spin current in general cases.

Apparent torsion in GR is due to tetrad anholonomy.

In teleparallel gravity, the only torsion is from anholonomy coefficients.

Abstract

In the general case, torsion couples to the spin current of the Dirac field. In General Relativity, the apparent torsion field to which the spin current of the Dirac field couples is a mere manifestation of the tetrad anholonomy. Seen from the tetrad frame itself, it has for components the anholonomy coefficients. The latter represent mechanical characteristics of the frame. In the teleparallel equivalent of General Relativity, this coefficient turns out to be the only torsion present.