A duality between curvature and torsion

TL;DR

This paper proposes a duality between curvature and torsion, unifies key length scales, and shows that torsion influences gravity at small scales, with testable predictions contrasting general relativity and teleparallel gravity.

Contribution

It introduces a duality between curvature and torsion, unifies length scales, and links general relativity and teleparallel gravity as limits of the ECSK theory.

Findings

Torsion weakens gravitational interaction at small scales.

Kerr-Newman black hole and electron share the same gyromagnetic ratio.

Small-scale torsion effects are testable with current technology.

Abstract

Compton wavelength and Schwarzschild radius are considered here as limiting cases of a unified length scale. Using this length, it is shown that the Dirac equation and the Einstein equations for a point mass are limiting cases of an underlying theory which includes torsion. We show that in this underlying theory the gravitational interaction between small masses is weaker than in Newtonian gravity. We explain as to why the Kerr-Newman black hole and the electron both have the same non-classical gyromagnetic ratio. We propose a duality between curvature and torsion and show that general relativity and teleparallel gravity are respectively the large mass and small mass limit of the ECSK theory. We demonstrate that small scale effects of torsion can be tested with current technology.