Fractal Threshold Behavior in Vacuum Gravitational Collapse

TL;DR

This paper provides numerical evidence of fractal threshold behavior in five-dimensional vacuum Einstein equations, showing how small changes can influence black hole formation, revealing complex dynamics near criticality.

Contribution

It demonstrates for the first time fractal threshold behavior in five-dimensional vacuum gravitational collapse using numerical simulations.

Findings

Fractal structure observed near the black hole formation threshold.

Small perturbations can significantly alter collapse outcomes.

Evidence of complex, butterfly-like sensitivity in gravitational collapse dynamics.

Abstract

We present the numerical evidence for fractal threshold behavior in the five dimensional vacuum Einstein equations satisfying the cohomogeneity-two triaxial Bianchi type-IX ansatz. In other words, we show that a flip of the wings of a butterfly may influence the process of the black hole formation.