Boundary dynamics in competing critical black hole formation

TL;DR

This paper investigates the boundary dynamics in black hole formation, revealing constant and varying critical exponents across different regions, and suggests the existence of a third critical solution influencing these behaviors.

Contribution

It provides a detailed numerical analysis of critical exponents in black hole formation boundaries, proposing the existence of a third critical solution affecting the dynamics.

Findings

The dominant exponent is constant across the Type II boundary, matching Choptuik's value.

The exponent varies across the Type I boundary, indicating different critical behavior.

Evidence suggests a third critical solution influences the boundary dynamics.

Abstract

Expanding upon our previous study of competing critical phenomena in black hole formation, we numerically investigate the behavior of dominant exponents across the boundary separating asymptotically dispersing and collapsing regions in a two-dimensional configuration space of initial data. We find that across the Type II boundary section the dominant exponent remains constant, equal to the reciprocal of Choptuik's well-known quasi-universal value, whereas across the Type I section the exponent noticeably varies. We postulate that this change reflects the existence of a third critical solution in addition to the two primary competing solutions, possibly another member of the family of metastable soliton stars constituting the Type I attractor.