https://doi.org/10.1140/epjp/s13360-026-07691-9
Regular Article
Weyl–Cosserat elasticity and gravitational memory: an effective microstructured model of spacetime
University of Strasbourg, Strasbourg, France
a
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Received:
20
February
2026
Accepted:
13
April
2026
Published online:
3
May
2026
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 nontrivial 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.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
