Critical phenomena in the collapse of quadrupolar and hexadecapolar gravitational waves

TL;DR

This paper presents numerical simulations of critical phenomena in vacuum gravitational wave collapse, revealing non-universal threshold solutions with approximate discrete self-similarity for quadrupolar and hexadecapolar initial data.

Contribution

It introduces a new numerical approach to study critical collapse of axisymmetric gravitational waves and compares threshold solutions for different multipolar initial data, showing no universal critical solution.

Findings

Threshold solutions show approximate discrete self-similarity.

Hexadecapolar threshold solution differs from quadrupolar one.

No universal critical solution exists for vacuum gravitational wave collapse.

Abstract

We report on numerical simulations of critical phenomena near the threshold of black hole formation in the collapse of axisymmetric gravitational waves in vacuum. We discuss several new features of our numerical treatment, and then compare results obtained from families of quadrupolar and hexadecapolar initial data. Specifically, we construct (nonlinear) initial data from quadrupolar and hexadecapolar, time-symmetric wavelike solutions to the linearized Einstein equations (often referred to as Teukolsky waves), and evolve these using a shock-avoiding slicing condition. While our degree of fine-tuning to the onset of black-hole formation is rather modest, we identify several features of the threshold solutions formed for the two families. Both threshold solutions appear to display an at least approximate discrete self-similarity with an accumulation event at the center, and the characteristics of the threshold solution for the quadrupolar data are consistent with those found previously by other authors. The hexadecapolar threshold solution appears to be distinct from the quadrupolar one, providing further support to the notion that there is no universal critical solution for the collapse of vacuum gravitational waves.