Choptuik Scaling and The Merger Transition

TL;DR

This paper explores the connection between Choptuik scaling and black-string black-hole mergers, revealing a shared critical solution structure, oscillation behaviors, and dimensional dependencies through analytic continuation and boundary condition analysis.

Contribution

It demonstrates a deep relationship between two critical phenomena in gravitational collapse and black hole physics, introducing a unified perspective via analytic continuation and boundary condition changes.

Findings

Critical solutions are related via double analytic continuation.

Off-critical oscillations are predicted for the merger system.

Scaling constants form a complex number, revealing underlying structure.

Abstract

The critical solution in Choptuik scaling is shown to be closely related to the critical solution in the black-string black-hole transition (the merger), through double analytic continuation, and a change of a boundary condition. The interest in studying various space-time dimensions D for both systems is stressed. Gundlach-Hod-Piran off-critical oscillations, familiar in the Choptuik set-up, are predicted for the merger system and are predicted to disappear above a critical dimension D*=10. The scaling constants, Delta(D), gamma(D), are shown to combine naturally to a single complex number.