EXACT COSMIC STRING SOLUTIONS BASED ON THE CONTINUUM THEORY OF DISLOCATIONS

Abstract

The effective action from the string compactification is studied on the manifolds with absolute parallelism. The cosmic strings can be described naturally by torsion formalism which has a direct analogy with dislocations in three-dimensional crystalline solids. We have found a stringy solution in a six-dimensional model on M4 × T2 which is compatible with that of Greene et al. and a cylindrically symmetric exact solution is obtained, which are different from the exact cosmic string solutions of the Einstein theory ever proposed. We have also obtained an exact solution in a four-dimensional model on M2 × T2 which can be considered as an example of the compactification on the noncompact manifold and may be expected to describe a space–time structure of our universe. The relation between the mass per unit length and the deficit angle is different from but can be consistent with that of the Einstein theory, since our solution could reproduce its prediction with a condition. We could also obtain the maximum value of the mass per unit length μ ~ 10−6 (~ 1022 g/cm ) by fine-tuning a parameter, which is consistent with recent observations. We have discussed the cosmic strings with the deficit angle larger than 2π.