Critical phenomena and a new class of self-similar spherically symmetric perfect-fluid solutions

We consider the self-similar solutions associated with the critical behavior observed in the gravitational collapse of spherically symmetric perfect fluids with the equation of state $p=\alpha \mu .$ We identify for the first time the global nature of these solutions and show that it is sensitive to the value of $\alpha .$ In particular, for $\alpha >0.28,$ 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.