Investigation into length scale dominance in critical black hole formation

The critical formation of low-mass black holes is a historical cornerstone of numerical general relativity, with important implications in cosmology for censorship conjectures and the production of primordial black holes (PBHs). Concurrent with the surge in black hole observational physics in recent years has been an increased interest in these subjects. Critical formation is often suggested as a mechanism for PBH production, but it is possible that the existence of different types of critical processes potentially accompanying more realistic scenarios may affect this conclusion more than has been considered thus far. This paper numerically investigates, as a toy model, the interplay of multiple near-critical fields in the collapse of spherically symmetric scalar fields. It is found that a combination of type I and type II near-critical fields results in a kind of competition between their respective critical evolutions. A heuristic explanation for this phenomenon is proposed employing ideas from the theory of dynamical systems.