Characteristic Critical Collapse of a Yang-Mills Field With Null Infinity

TL;DR

This study investigates the critical gravitational collapse of a Yang-Mills field using characteristic evolution, revealing universal discrete self-similarity and mass scaling near black hole formation threshold.

Contribution

It introduces a fourth-order accurate numerical method in compactified Bondi coordinates to analyze global quantities and confirms universality and DSS behavior in Yang-Mills collapse.

Findings

DSS behavior with echoing period ~0.7388 confirmed

Black hole mass scales with critical exponent ~0.1977

Results are universal across different initial data

Abstract

Solutions to the Einstein equations near the threshold of black hole formation exhibit remarkable behavior known as critical phenomena gravitational collapse. In this work we perform characteristic evolution in compactified Bondi coordinates in order to study the critical collapse of a Yang-Mills field, allowing for the extraction of global quantities such as the Bondi mass and news function. Our numerical approach is fourth-order accurate. First, we demonstrate that the collapsing field exhibits local DSS behavior, characterized by an echoing period of~$\Delta \simeq 0.7388$, agreeing with previous works up to the second decimal place. We find that global quantities such as the Bondi mass and news function display the same DSS behavior. We furthermore show that the mass of the black holes formed during near-threshold evolutions scales as a function of the distance to the critical parameter, with a critical exponent of approximately~$\gamma=0.1977\pm0.0009$. Finally, our findings indicate that these results are universal, irrespective of the initial data.