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 a >0.28, we show that the critical solutionis associated with a new class of asymptotically Minkowski self-similar spacetimes. We discuss some of the implications of this for critical phenomena.