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

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.