Einstein-Cartan theory as a theory of defects in space-time

TL;DR

This paper draws an analogy between Einstein-Cartan theory of gravitation and defect theory in elastic media, using their shared geometrical foundations to deepen understanding of space-time torsion and curvature.

Contribution

It introduces a formal analogy between space-time with torsion and defects in elastic media, enhancing conceptual understanding of Einstein-Cartan theory.

Findings

Space-time with curvature and torsion can be viewed as a continuum with defects.

The analogy helps illustrate the geometrical concept of torsion.

Shared geometrical basis clarifies the foundations of both theories.

Abstract

The Einstein-Cartan theory of gravitation and the classical theory of defects in an elastic medium are presented and compared. The former is an extension of general relativity and refers to four-dimensional space-time, while we introduce the latter as a description of the equilibrium state of a three-dimensional continuum. Despite these important differences, an analogy is built on their common geometrical foundations, and it is shown that a space-time with curvature and torsion can be considered as a state of a four-dimensional continuum containing defects. This formal analogy is useful for illustrating the geometrical concept of torsion by applying it to concrete physical problems. Moreover, the presentation of these theories using a common geometrical basis allows a deeper understanding of their foundations.