Teleparallel Spin Connection

TL;DR

This paper introduces a new covariant spin connection expression for teleparallel gravity, establishing its full equivalence to general relativity, including in the presence of spinor fields.

Contribution

It proposes a novel spin connection formulation for teleparallel gravity that ensures covariance and equivalence with general relativity.

Findings

The new spin connection is given by minus the contorsion tensor plus a zero connection.

The minimal coupling becomes covariant under local Lorentz transformations.

Teleparallel gravity is shown to be fully equivalent to general relativity with this formulation.

Abstract

A new expression for the spin connection of teleparallel gravity is proposed, given by minus the contorsion tensor plus a zero connection. The corresponding minimal coupling is covariant under local Lorentz transformation, and equivalent to the minimal coupling prescription of general relativity. With this coupling prescription, therefore, teleparallel gravity turns out to be fully equivalent to general relativity, even in the presence of spinor fields.