Two-step spacetime deformation induced dynamical torsion

TL;DR

This paper develops a two-step spacetime deformation framework to establish a dynamical torsion theory within Einstein-Cartan gravity, enabling propagating torsion and short-range spin-spin interactions.

Contribution

It introduces a novel two-step deformation approach to formulate a dynamical torsion theory, extending Einstein-Cartan gravity with propagating torsion.

Findings

Standard EC torsion equations are algebraic and non-propagating.

Modified EC equations allow for dynamical, propagating torsion.

The theory predicts short-range spin-spin interactions.

Abstract

We extend the geometrical ideas of the spacetime deformations to study the physical foundation of the post-Riemannian geometry. To this aim, we construct the theory of 'two-step spacetime deformation' as a guiding principle. We address the theory of teleparallel gravity and construct a consistent Einstein-Cartan (EC) theory with the 'dynamical torsion'. We show that the equations of the standard EC theory, in which the equation defining torsion is the algebraic type and, in fact, no propagation of torsion is allowed, can be equivalently replaced by the set of 'modified EC equations' in which the torsion, in general, is dynamical. The special physical constraint imposed upon the spacetime deformations yields the short-range propagating spin-spin interaction.