On the embedding of spacetime in higher-dimensional spaces with torsion

TL;DR

This paper explores how spacetime with torsion can be embedded in higher-dimensional spaces, affecting particle confinement and stability, and introduces a classical analogue of quantum confinement through torsion fields.

Contribution

It extends Riemannian theorems to Riemann-Cartan geometries and demonstrates local isometric embeddings of torsioned spacetimes, linking torsion to confinement phenomena.

Findings

Torsion influences geodesic confinement near branes.

Embedding spacetime with torsion is feasible in warped product spaces.

Torsion can mimic quantum confinement effects in a classical framework.

Abstract

We revisit the Riemann-Cartan geometry in the context of recent higher-dimensional theories of spacetime. After introducing the concept of torsion in a modern geometrical language we present some results that represent extensions of Riemannian theorems. We consider the theory of local embeddings and submanifolds in the context of Riemann-Cartan geometries and show how a Riemannian spacetime may be locally and isometrically embedded in a bulk with torsion. As an application of this result, we discuss the problem of classical confinement and the stability of motion of particles and photons in the neighbourhood of branes for the case when the bulk has torsion. We illustrate our ideas considering the particular case when the embedding space has the geometry of a warped product space . We show how the confinement and stability properties of geodesics near the brane may be affected by the torsion of the embedding manifold. In this way we construct a classical analogue of quantum confinement inspired in theoretical-field models by replacing a scalar field with a torsion field.