A New Tradition between Discrete and Contiuous Self-Similarity in Critical 
Gravitational Collapse

Lechner, Christiane; Thornburg, Jonathan; Husa, Sascha; Aichelburg, Peter C.

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A New Tradition between Discrete and Contiuous Self-Similarity in Critical Gravitational Collapse

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Lechner, Christiane
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Thornburg, Jonathan
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Husa, Sascha
Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Lechner, C., Thornburg, J., Husa, S., & Aichelburg, P. C. (2002). A New Tradition between Discrete and Contiuous Self-Similarity in Critical Gravitational Collapse. Physical Review D, 65: 081501.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-541E-0

Abstract

We analyze a bifurcation phenomenon associated with critical gravitational collapse in a family of self-gravitating SU(2) sigma models. As the dimensionless coupling constant decreases, the critical solution changes from discretely self-similar (DSS) to continuously self-similar (CSS). Numerical results provide evidence for a bifurcation which is analogous to a heteroclinic loop bifurcation in dynamical systems, where two fixed points (CSS) collide with a limit cycle (DSS) in phase space as the coupling constant tends to a critical value.