It was pointed out that topological defects in solids, which were usually described using complicated boundary conditions in elastic theory, could be described more simply as being sources of a gravity-like deformation field in the Katanaev-Volovich geometrical approach. In the latter method, the deformation field was described by a non-Euclidean metric which incorporated the boundary conditions that were imposed by the defects. One possible means of gaining some insight into the motion of particles in a medium containing topological defects (such as electrons in a dislocated metal) was to look at the geodesics of the medium around the defect. An exact solution was found here for the geodesic equation for an elastic medium containing a generic line defect: the dispiration. This could be either a screw dislocation or a wedge disclination, depending upon the choice of parameters.

Geodesics around Line Defects in Elastic Solids. A.De Padua, F.Parisio-Filho, F.Moraes: Physics Letters A, 1998, 238[2-3], 153-8