Wedge dislocations and three-dimensional gravity

The expression for the free energy of arbitrary static distribution of wedge dislocations in elastic media is proposed. In the framework of geometric theory of defects, the free energy is given by the Euclidean action for (1+2)-dimensional gravity interacting with N point particles. Relative movement of particles in gravity corresponds to bending of dislocations. The equations of equilibrium are obtained and analyzed. For two dislocations, the solution is found explicitly through hypergeometric functions.