Critical Phenomena in Nonlinear Sigma Models
Steven L. Liebling, Eric W. Hirschmann, James Isenberg
Abstract
We consider solutions to the nonlinear sigma model (wave maps) with target space S3 and base space 3+1 Minkowski space, and we find critical behavior separating singular solutions from nonsingular solutions. For families of solutions with localized spatial support a self-similar solution is found at the boundary. For other families, we find that a static solution appears to sit at the boundary. This behavior is compared to the black hole critical phenomena found by Choptuik.
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