Torsional Monopoles and Torqued Geometries in Gravity and Condensed Matter

TL;DR

This paper introduces torsional monopoles in gravity and condensed matter, revealing topologically conserved torsion configurations that resemble monopoles and generalize the Cartan spiral staircase, with implications for both fields.

Contribution

It identifies a class of torsion configurations with integer topological charge, supporting monopole solutions in gravity and condensed matter systems.

Findings

Torsional monopoles have a conserved, integer-valued topological charge.

These monopoles can exist in gravity models with curvature.

They can be modeled as defects in condensed matter systems.

Abstract

Torsional degrees of freedom play an important role in modern gravity theories as well as in condensed matter systems where they can be modeled by defects in solids. Here we isolate a class of torsion models that support torsion configurations with a localized, conserved charge that adopts integer values. The charge is topological in nature and the torsional configurations can be thought of as torsional `monopole' solutions. We explore some of the properties of these configurations in gravity models with non-vanishing curvature, and discuss the possible existence of such monopoles in condensed matter systems. To conclude, we show how the monopoles can be thought of as a natural generalization of the Cartan spiral staircase.