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          Institute: MPI für Gravitationsphysik     Collection: Geometric Analysis and Gravitation     Display Documents

ID: 3369.0, MPI für Gravitationsphysik / Geometric Analysis and Gravitation
Type II Critical Collapse of a Self-Gravitating Nonlinear Sigma Model
Authors:Husa, Sascha; Lechner, Christiane; Pürrer, Michael; Thornburg, Jonathan; Aichelburg, Peter C.
Date of Publication (YYYY-MM-DD):2000
Title of Journal:Physical Review D
Sequence Number of Article:104007
Review Status:Peer-review
Audience:Not Specified
Abstract / Description: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 outgoing–null-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.
External Publication Status:published
Document Type:Article
Communicated by:Gerhard Huisken
Affiliations:MPI für Gravitationsphysik/Geometric Analysis and Gravitation
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