# Critical phenomena in gravitational collapse with two competing massless matter fields

## TL;DR

This paper investigates how two different matter fields, scalar and Yang-Mills, interact during gravitational collapse, revealing a shared quasi-discrete self-similar critical solution that dominates at small scales.

## Contribution

It introduces the concept of a quasi-discretely self-similar solution that unifies the critical behavior of two matter fields in gravitational collapse.

## Key findings

- Scalar field dominates at small scales during collapse.
- Existence of a shared QSS critical solution for both fields.
- QSS has only one unstable mode, acting as the critical solution.

## Abstract

In the gravitational collapse of matter beyond spherical symmetry, gravitational waves are necessarily present. On the other hand, gravitational waves can collapse to a black hole even without matter. One might therefore wonder whether the interaction and competition between the matter fields and gravitational waves affects critical phenomena at the threshold of black hole formation. As a toy model for this, we study type II critical collapse with two matter fields in spherical symmetry, namely a scalar field and a Yang-Mills field. On their own, both display discrete self-similarity (DSS) in type II critical collapse, and we can take either one of them as a toy model for gravitational waves. To our surprise, in numerical time evolutions we find that, for sufficiently good fine-tuning, the scalar field always dominates on sufficiently small scales. We explain our results by the conjectured existence of a "quasi-discretely self-similar" (QSS) solution shared by the two fields, equal to the known Yang-Mills critical solution at infinitely large scales and the known scalar field critical solution (the Choptuik solution) at infinitely small scales, with a gradual transition from one field to the other. This QSS solution itself has only one unstable mode, and so acts as the critical solution for any mixture of scalar field and Yang-Mills initial data.