Teleparallel orthonormal frames constraints on torsion detection?

TL;DR

This paper investigates constraints on torsion detection in teleparallel gravity, showing incompatibility with certain spin-polarized solutions and exploring alternative geometries and tetrad choices.

Contribution

It demonstrates the incompatibility of spin-polarized cylindrically symmetric solutions with teleparallel gravity and proposes alternative geometries and tetrad configurations.

Findings

Spin-polarized solutions are incompatible with teleparallel gravity.

A cylindrically symmetric Riemannian solution with conical defects is obtained.

The choice of spin distribution affects the compatibility with teleparallel constraints.

Abstract

Spin-polarised cylindrically symmetric solution are shown not to be compatible with teleparallel gravity.This can be done in two distinct manners.The first is to show that not all components of the orthonormal tetrad (OT).It is argue however that this result maybe done by a bad choice of the spin distribution along the cylinder.A cylindrically symmetric Riemannian solution is obtained which represents a conical geometry of defects.