Type II critical collapse of a self-gravitating nonlinear sigma model - art. no. 104007

We report on the existence and phenomenology of type II critical collapse w ithin the one-parameter family of SU(2) sigma models coupled to gravity. Nu merical investigations in spherical symmetry show discretely self-similar ( DSS) behavior at the threshold of black hole formation for values of the di mensionless coupling constant eta ranging from 0.2 to 100; at 0.18 we see s mall deviations from DSS. While the echoing period h of the critical soluti on rises sharply towards the lower limit of this range, the characteristic mass scaling has a critical exponent gamma which is almost independent of e ta, asymptoting to 0.1185 +/- 0.0005 at large eta. We also find critical sc aling of the scalar curvature for near-critical initial data. Our numerical results are based on an outgoing-null-cone formulation of the Einstein-mat ter equations, specialized to spherical symmetry. Our numerically computed initial-data critical parameters p* show second order convergence with the grid resolution, and after compensating for this variation in p*, our indiv idual evolutions are uniformly second order convergent even very close to c riticality.