The Singularity Threshold of the Nonlinear Sigma Model Using 3D Adaptive Mesh Refinement

摘要

Numerical solutions to the nonlinear sigma model (NLSM), a wave map from 3+1Minkowski space to S^3, are computed in three spatial dimensions (3D) usingadaptive mesh refinement (AMR). For initial data with compact support the modelis known to have two regimes, one in which regular initial data forms asingularity and another in which the energy is dispersed to infinity. Thetransition between these regimes has been shown in spherical symmetry todemonstrate threshold behavior similar to that between black hole formation anddispersal in gravitating theories. Here, I generalize the result by removingthe assumption of spherical symmetry. The evolutions suggest that thespherically symmetric critical solution remains an intermediate attractorseparating the two end states.