Direct SMBH Formation Driven by Runaway Stellar Collisions in Globally Unstable Stellar Systems

ABSTRACT The fueling problem addresses the ultimate fate of the reservoirs of gas and stars driven into the deepest gravitational potential wells of galaxies, thus it may contain the Universe's densest concentrations of gas and stars. This raises a key question: does the infalling material collapse directly into a supermassive black hole, or can it first settle into another stable configuration? Dense star clusters are strong candidates, there is a critical threshold beyond which the cluster becomes quickly unstable and transforms into an SMBH. In this work, we synthesize theoretical, numerical, and observational evidence supporting a scenario where runaway stellar collisions drive the global collapse of dense stellar clusters. We identify a critical regime in which the timescale for stellar collisions becomes shorter than the dynamical relaxation timescale, triggering global instabilities that drive the rapid collapse of compact stellar systems. In this regime, runaway mergers produce a very massive star that later collapses into a black hole seed. We demonstrate that this purely collisional channel is viable across a wide range of cluster types. Finally, we propose that little red dots may exist in a transient, collision‐dominated phase, in which the rapid formation of massive black hole seeds is likely inevitable.