The geodesic rule and the spectrum of the vacuum
  We analyze the consequences of a recent argument justifying the validity of the "geodesic rule" which can be used to determine the density of global topological defects. We derive a formula that provides a rough estimate of the number of string-like defects formed in a phase transition. We apply this formula to vacua which are spheres. We provide some reasons for the deviation of our predictions from the corresponding accepted values. 
Nikos Kalogeropoulos