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Journal Article

#### Type II Critical Collapse of a Self-Gravitating Nonlinear Sigma Model

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##### Citation

Husa, S., Lechner, C., Pürrer, M., Thornburg, J., & Aichelburg, P. C. (2000). Type
II Critical Collapse of a Self-Gravitating Nonlinear Sigma Model.* Physical Review D,* *62*: 104007.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-57C4-B

##### Abstract

We report on the existence and phenomenology of type II critical collapse within the one-parameter family of SU(2) sigma models coupled to gravity. Numerical investigations in spherical symmetry show discretely self-similar (DSS) behavior at the threshold of black hole formation for values of the dimensionless coupling constant eta ranging from 0.2 to 100; at 0.18 we see small deviations from DSS. While the echoing period Delta of the critical solution rises sharply towards the lower limit of this range, the characteristic mass scaling has a critical exponent gamma which is almost independent of eta, asymptoting to 0.1185ą0.0005 at large eta. We also find critical scaling of the scalar curvature for near-critical initial data. Our numerical results are based on an outgoingnull-cone formulation of the Einstein-matter 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 individual evolutions are uniformly second order convergent even very close to criticality.