Geodesic incompleteness in the CP1 model on a compact Riemann surface
L. A. Sadun, J. M. Speight
Abstract
It is proved that the moduli space of static solutions of the CP1 model on spacetime Sigma x R, where Sigma is any compact Riemann surface, is geodesically incomplete with respect to the metric induced by the kinetic energy functional. The geodesic approximation predicts, therefore, that lumps can collapse and form singularities in finite time in these models.
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