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Choptuik scaling and the scale invariance of Einstein's equation

David Garfinkle
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Abstract

The relationship of Choptuik scaling to the scale invariance of Einstein's equation is explored. Ordinary dynamical systems often have limit cycles: periodic orbits that are the asymptotic limit of generic solutions. We show how to separate Einstein's equation into the dynamics of the overall scale and the dynamics of the ``scale invariant'' part of the metric. Periodicity of the scale invariant part implies periodic self-similarity of the spacetime. We also analyze a toy model that exhibits many of the features of Choptuik scaling.

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David Garfinkle. 1997-07-31. Choptuik scaling and the scale invariance of Einstein's equation. https://doi.org/10.1103/physrevd.56.3169

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