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

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.