It was recalled that one method for obtaining some insight into the motion of particles in a medium with topological defects (such as electrons in a dislocated metal) was to look at the geodesics of the medium around the defect. The Hamilton-Jacobi equation for the geodesics in a continuous medium which contained a torsional defect (edge dislocation) was solved here by using perturbation theory to first order in the Burgers vector.

Geodesics around a Dislocation. F.Moraes: Physics Letters A, 1996, 214[3-4], 189-92