Fine-Structure of Choptuik's Mass-Scaling Relation

Abstract

We conjecture (analytically) and demonstrate (numerically) the existence of a fine-structure above the power-law behavior of the mass of black-holes that form in gravitational collapse of spherical massless scalar field. The fine-structure is a periodic function of the critical-separation $(p-p^*)$. We predict that the period $\varpi$ is {\it universal} and that it depends on the previous universal parameters, the critical exponent, $β$, and the echoing period $Δ$ as $\varpi = Δ/β$.

9 pages and 3 figures, submitted to Physical Review Letters Complete PS file is available at ftp://shemesh.fiz.huji.ac.il or at http://shemesh.fiz.huji.ac.il/papers/hp.uu Revised version included clearer figures