Fine-Structure of Choptuik's Mass-Scaling Relation

TL;DR

This paper investigates the detailed structure of black hole mass scaling near critical collapse, revealing a universal periodic fine-structure dependent on critical parameters through analytical and numerical methods.

Contribution

It introduces the concept of a universal fine-structure in Choptuik's mass-scaling relation and derives its dependence on critical parameters.

Findings

Discovery of a periodic fine-structure in mass scaling.

Universal period related to critical exponent and echoing period.

Numerical and analytical evidence supporting the conjecture.

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, $\beta$, and the echoing period $\Delta$ as $\varpi = \Delta /\beta$.