Type II critical collapse of a self-gravitating nonlinear σ model

Husa, Sascha, Lechner, Christiane, Pürrer, Michael, Thornburg, Jonathan and Aichelburg, Peter 2000. Type II critical collapse of a self-gravitating nonlinear σ model. Physical Review D - Particles, Fields, Gravitation and Cosmology 62 (10) , 104007. 10.1103/PhysRevD.62.104007

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Abstract

We report on the existence and phenomenology of type II critical collapse within the one-parameter family of SU(2) σ 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 η ranging from 0.2 to 100; at 0.18 we see small deviations from DSS. While the echoing period Δ of the critical solution rises sharply towards the lower limit of this range, the characteristic mass scaling has a critical exponent γ which is almost independent of η, asymptoting to 0.1185±0.0005 at large η. 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 show second order convergence with the grid resolution, and after compensating for this variation in our individual evolutions are uniformly second order convergent even very close to criticality.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Physics and Astronomy
Subjects:	Q Science > QC Physics
Publisher:	American Physical Society
ISSN:	0556-2821
Last Modified:	19 Oct 2019 03:40
URI:	https://orca.cardiff.ac.uk/id/eprint/58079

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