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Episodic Self-Similarity in Critical Gravitational Collapse

J. Thornburg·Ch. Lechner·M. Purrer·P. C. Aichelburg·S. Husa
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Abstract

We report on a new behavior found in numerical simulations of spherically symmetric gravitational collapse in self-gravitating SU(2) sigma models at intermediate gravitational coupling constants: The critical solution (between black hole formation and dispersion) closely approximates the continuously self-similar (CSS) solution for a finite time interval, then departs from this, and then returns to CSS again. This cycle repeats several times, each with a different CSS accumulation point. We have preliminary evidence that this same critical solution is also discretely self-similar (DSS) between the CSS episodes, but with an echoing period $Δ$ which varies during the evolution.

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J. Thornburg, Ch. Lechner, M. Purrer, P. C. Aichelburg, S. Husa. 2000-12-12. Episodic Self-Similarity in Critical Gravitational Collapse. https://arxiv.org/abs/gr-qc/0012043

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