Exact solutions for cosmic strings in closed universes

Vacuum spacetimes with two-parameter symmetry groups have been investigated with the presence of strings along the two symmetry axes. The simplest spacetime metrics of this type are given explicitly. These spacetimes model closed (three-sphere space topology) gravitational-wave-dominated universes with long straight strings whose mass per unit length can have any value. Because the strings sit at the symmetry axes, they have no local effects on the evolution of the spacetime or the motion of test particles in it. However, the strings do have global effects—they cause a constant rescaling of time which affects the expansion rate in these models. Contrary to the usual arguments, these long straight strings do not seem to evolve so as to dominate these radiation-dominated universes.