GRAVITY AND CRYSTALLINE DEFECTS

The analog models of gravity presented in this session are unable to account for the full geometric structure of spacetime. The purpose of this lecture is to point out that a perfect analog can be achieved by imagining the world to be a crystal at the Planckian length scale (world crystal). The defects in this crystal have precisely the degrees of freedom of a Riemann-Cartan geometry. Disclinations characterize the curvature content, dislocations the torsion content of the spacetime. The memory of the crystal structure is lost by quantum uctuations of the Kostelitz-Thouless type. In the region of high curvature, the defects are so dense that the crystal melts and spacetime aquires completely novel properties. On the world lattice, quantum mechanics become classical at Planck scales modifying significantly the properties of mini-black holes.