Quasi-regular singularities and cosmic strings

Abstract

It is shown that a general two-dimensional timelike quasi-regular singularity has the same energy-momentum tensor as a straight conical cosmic string. Conversely any model of a cosmic string in which the energy-momentum is concentrated on a 2-surface and the curvature is sufficiently regular must be described by a quasi-regular singularity. It is shown that the direction of such a singularity is a fixed point of the holonomy group generated by parallel propagation around loops encircling the singularity and that the holonomy at two different points is the same. This is used to show that such singularities are totally geodesic. The implications for constraints on the dynamics of cosmic strings are discussed.