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A New Transition between Discrete and Continuous Self-Similarity in Critical Gravitational Collapse

Christiane Lechner·Jonathan Thornburg·Sascha Husa·Peter C. Aichelburg
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Abstract

We analyze a bifurcation phenomenon associated with critical gravitational collapse in a family of self-gravitating SU(2) $σ$-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.

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Christiane Lechner, Jonathan Thornburg, Sascha Husa, Peter C. Aichelburg. 2001-12-07. A New Transition between Discrete and Continuous Self-Similarity in Critical Gravitational Collapse. https://doi.org/10.1103/physrevd.65.081501

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