Geodesics around line defects in elastic solids

Topological defects in solids, usually described by complicated boundary conditions in elastic theory, may be described more simply as sources of a gravity- like deformation field in the geometric approach of Katanaev and Volovich. This way, the deformation field is described by non-Euclidean metric that incorporates the boundary imposed by the defects. A possible way of gaining some insight into the motion of particles in a medium with topological defects (e.g., electrons in a dislocated metal) is to look at the geodesics of the medium around the defect. In this work, we find the exact solution for the geodesic equation for elastic medium with a generic line defect, the dispiration, that can either be a screw dislocation or a wedge disclination for particular choices of its parameters.