COSMIC STRINGS IN BIANCHI-II, BIANCHI-VIII AND BIANCHI-IX SPACETIMES - INTEGRABLE CASES

We investigate the integrability of cosmic strings in Bianchi II, VIII and IX spacetimes using a Lie symmetry analysis. The behaviour of the gravitational field is governed by solutions of a single second order nonlinear differential equation. We demonstrate that this equation is integrable and admits an infinite family of physically reasonable sol utions. Particular solutions obtained by other authors are shown to be special cases of our class of solutions.