Codimension-two critical behavior in vacuum gravitational collapse

TL;DR

This paper investigates the critical behavior in five-dimensional vacuum gravitational collapse, predicting and confirming a codimension-two attractor characterized by a discretely self-similar solution with two unstable modes.

Contribution

It predicts and numerically confirms a novel codimension-two attractor in vacuum gravitational collapse with a specific symmetry and self-similarity.

Findings

Identification of a discretely self-similar solution as the codimension-two attractor

Confirmation of the attractor's existence through numerical methods

Discovery of two unstable modes associated with the attractor

Abstract

We consider the critical behavior at the threshold of black hole formation for the five dimensional vacuum Einstein equations satisfying the cohomogeneity-two triaxial Bianchi IX ansatz. Exploiting a discrete symmetry present in this model we predict the existence of a codimension-two attractor. This prediction is confirmed numerically and the codimension-two attractor is identified as a discretely self-similar solution with two unstable modes.