Adaptive Event Horizon Tracking and Critical Phenomena in Binary Black Hole Coalescence

TL;DR

This paper introduces a computational method to study black hole mergers, revealing critical phenomena such as power law scaling in the minimal throat during coalescence, supported by analytical confirmation.

Contribution

Develops and validates a new event horizon tracking solver applied to black hole mergers, demonstrating critical phenomena and power law behavior in axisymmetric cases.

Findings

Power law scaling of minimal throat during merger

Confirmation of critical phenomena analytically

Potential universality beyond specific solutions

Abstract

This work establishes critical phenomena in the topological transition of black hole coalescence. We describe and validate a computational front tracking event horizon solver, developed for generic studies of the black hole coalescence problem. We then apply this to the Kastor - Traschen axisymmetric analytic solution of the extremal Maxwell - Einstein black hole merger with cosmological constant. The surprising result of this computational analysis is a power law scaling of the minimal throat proportional to time. The minimal throat connecting the two holes obeys this power law during a short time immediately at the beginning of merger. We also confirm the behavior analytically. Thus, at least in one axisymmetric situation a critical phenomenon exists. We give arguments for a broader universality class than the restricted requirements of the Kastor - Traschen solution.