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

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.

18 pages, 7 EPS figures, RevTeX4, to appear in the American Journal of Physics, revised version with typos corrected

Cited by in corpus (24)

• The Srni lectures on non-integrable geometries with torsion
• Plasticity in amorphous solids is mediated by topological defects in the displacement field
• Constraining f(T) gravity in the Solar System
• Cosmic strings in $f\left(R,L_m\right)$ gravity
• Deformations, relaxation and broken symmetries in liquids, solids and glasses: a unified topological field theory
• Cartan's spiral staircase in physics and, in particular, in the gauge theory of dislocations
• Einstein-Cartan Theory
• Elie Cartan's torsion in geometry and in field theory, an essay
• Gravito-magnetic resonance in the field of a gravitational wave
• Torsional Monopoles and Torqued Geometries in Gravity and Condensed Matter
• Torsion at different scales: from materials to the Universe
• Volume elements and torsion
• Quantum solitodynamics: Non-linear wave mechanics and pilot-wave theory
• Canonical Quantization of Crystal Dislocation and Electron-Dislocation Scattering in an Isotropic Medium
• An assessment of Evans' unified field theory II
• An assessment of Evans' unified field theory I
• Effects of gravitational waves on electromagnetic fields
• Some geometrical aspects of gravitational waves using continuum mechanics analogy: State of the art and potential consequences
• Analogy of space-time as an elastic medium -- Study of the perturbation tensor of the metric $h_{\mu \nu }$ through the prism of the analogy of the theory of elasticity -- Analysis and potential consequences
• Weyl Cosserat Elasticity and Gravitational Memory: An Effective Microstructured Model of Spacetime
• A Cosmological Bragg Law: Interpreting the CMB as a Diffractogram of Foliated Spacetime
• Time-loops to spot torsion on bidimensional Dirac materials with dislocations
• How the Modified Bertrand Theorem Explains Regularities and Anomalies of the Periodic Table of Elements
• Einstein manifolds with skew torsion