Weyl Cosserat Elasticity and Gravitational Memory: An Effective Microstructured Model of Spacetime

TL;DR

This paper develops a microstructured elastic model of spacetime linking gravitational memory to topological defects, providing a new perspective on gravitational phenomena through Cosserat elasticity.

Contribution

It explicitly constructs a correspondence between Weyl tensor components and micropolar elastic medium kinematics, extending Einstein Cartan theory with propagating torsion modes.

Findings

Reinterprets gravitational memory as topological dislocation charge.

Derives the correspondence from Bianchi identities and geodesic deviation.

Constructs an effective Lagrangian describing propagating torsion modes.

Abstract

We construct a mathematically controlled correspondence between the electric and magnetic parts of the Weyl tensor in vacuum general relativity and the kinematics of a micropolar (Cosserat) elastic medium. In this framework, gravitational memory is reinterpreted as the topological charge of an effective dislocation field in spacetime. The ordinary displacement memory corresponds to an edge dislocation characterized by a non trivial Burgers vector, while spin memory corresponds to a screw type defect associated with rotational mismatch. We formulate the correspondence explicitly, derive it from the Bianchi identities and the geodesic deviation equation, and construct an effective Lagrangian extension of Einstein Cartan theory describing propagating torsion modes. The framework is shown to be an effective coarse-grained description rather than a modification of classical GR, and we discuss its observational viability.