2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/190251We consider the self-similar solutions associated with the critical behavior observed in the gravitational collapse of spherically symmetric perfect fluids with equation of state $p=αμ$. We identify for the first time the global nature of these solutions and show that it is sensitive to the value of $α$. In particular, for $α>0.28$, we show that the critical solution is associated with a new class of asymptotically Minkowski self-similar spacetimes. We discuss some of the implications of this for critical phenomena.5 pages RevTeX, 5 eps figuresGeneral Relativity and Quantum Cosmologytext