Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2002-02-26
Phys.Rev. D66 (2002) 041703
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
5 pages, 5 figures, 1 table; To be published in Phys. Rev. D.; Added discussion of initial data; Added figure and references
Scientific paper
10.1103/PhysRevD.66.041703
Numerical solutions to the nonlinear sigma model (NLSM), a wave map from 3+1 Minkowski space to S^3, are computed in three spatial dimensions (3D) using adaptive mesh refinement (AMR). For initial data with compact support the model is known to have two regimes, one in which regular initial data forms a singularity and another in which the energy is dispersed to infinity. The transition between these regimes has been shown in spherical symmetry to demonstrate threshold behavior similar to that between black hole formation and dispersal in gravitating theories. Here, I generalize the result by removing the assumption of spherical symmetry. The evolutions suggest that the spherically symmetric critical solution remains an intermediate attractor separating the two end states.
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