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The chain of events usually understood to lead to the formation oftopological defects during phase transitions is known as the Kibble mechanism.A central component of the mechanism is the so-called ``geodesic rule''.Although in the Abelian Higgs model the validity of the geodesic rule has beenquestioned recently, it is known to be valid on energetic grounds for a globalU(1) symmetry breaking transition. However, even for these globally symmetricmodels no dynamical analisys of the rule has been carried to this date, andsome points as to how events proceed still remain obscure. This paper tries toclarify the dynamics of the geodesic rule in the context of a global U(1)model. With an appropriate ansatz for the field modulus we find a family ofanalytical expressions, phase walls, that accounts for both geodesic andnongeodesic configurations. We then show how the latter ones are unstable anddecay into the former by nucleating pairs of defects. Finnally, we try to givea physical perspective of how the geodesic rule might really work in thesetransitions.Comment: 10 pages, 9 multiple figre

How does the geodesic rule really work for global symmetry breaking first order phase transitions?