Scattering on Dislocations and Cosmic Strings in the Geometric Theory of Defects

Abstract

We consider scattering of elastic waves on parallel wedge dislocations in the geometric theory of defects or, equivalently, scattering of point particles and light rays on cosmic strings. Dislocations are described as torsion singularities located on parallel lines, and trajectories of phonons are assumed to be the corresponding extremals. Extremals are found for arbitrary distribution of the dislocations in the monopole, dipole, and quadrupole approximation and the scattering angle is obtained. Examples of continuous distribution of wedge and edge dislocations are considered. We have found that for deficit angles close to −2 πa star located behind a cosmic string may have any even number of images, 2, 4, 6, … The close relationship between dislocations and conformal maps is elucidated in detail.