Critical behavior in vacuum gravitational collapse in 4+1 dimensions

TL;DR

This paper demonstrates that in 4+1 dimensions, vacuum Einstein equations admit radially symmetric gravitational waves that undergo critical collapse, exhibiting discretely self-similar Type II behavior at black hole formation threshold.

Contribution

It reveals the existence of gravitational waves with radial symmetry in higher dimensions and analyzes their critical collapse behavior numerically.

Findings

Discovered gravitational waves in 4+1 dimensions with radial symmetry.

Observed discretely self-similar Type II critical behavior during collapse.

Numerical evidence of black hole formation threshold in higher-dimensional vacuum spacetimes.

Abstract

We show that the 4+1 dimensional vacuum Einstein equations admit gravitational waves with radial symmetry. The dynamical degrees of freedom correspond to deformations of the three-sphere orthogonal to the $(t,r)$ plane. Gravitational collapse of such waves is studied numerically and shown to exhibit discretely self-similar Type II critical behavior at the threshold of black hole formation.