COLLAPSE OF SPHERICALLY SYMMETRICAL TEXTURES

We examine the collapse of spherically symmetric texture configurations without resort to a sigma-model approximation, in both Minkowski and Friedmann universes. Relations between topological charge and unwinding time are found, and it is demonstrated that while any texture of topological charge Q > 0.5 can in principle unwind, one expects the generic unwinding events to involve a characteristic, background-dependent charge. In Minkowski, radiation-, and matter-dominated universes we find that unwindings typically involve charges of Q approximately 0.74, 0.82, and 0.89, respectively. We also investigate the attainability of self-similarity (on which the only known analytic solution is based) in the evolution of textures, and demonstrate analytically that exact self-similar solutions in flat space exist only for an integer topological charge.