Critical Behavior of Black Hole Formation in a Scalar Wave Collapse
  We present a self-similar model of spherically symmetric collapse of a massless scalar field with a parameter $p$. The black hole formation is explicitly shown to occur only in the strong-field implosion of $p >1$. The field evolution in the critical limit $ p \rightarrow 1 $ is compared with numerical results found by Choptuik. 
Y.Oshiro, K.Nakamura and A.Tomimatsu